Construction Master 5: Right Triangle Trigonometry

Construction Master 5:   Right Triangle Trigonometry

Solving Right Triangles

The Construction Master 5 has four keys that allow the user to solve right triangles.  The four keys involved are:

[ Rise ] : The rise of the triangle, opposite side (Y).  The value entered can have units.

[ Run ] : The run of the triangle, adjacent side (X).  The value entered can have units.  

[ Diag ] : The diagonal of the triangle, hypotenuse (R).  The value entered can have units.  

[ Pitch ]: Can have one of four values: pitch  (rise in inches over a run of 12 inches), angle (in degrees), slope (rise/run), and grade (percent representation of the slope).

There are four types of entry with the [ Pitch ] key, as stated by the Construction Master 5's Pocket Reference Guide:

1.  n [ Inch ] [ Pitch ] enters the angle as a pitch:  n inch rise over 12 inch run, used in construction and industry mathematics 

2.  Θ (no units attached) [ Pitch ] enters the angle as angle degrees

3.  r [ Conv ] [ Pitch ] enters the value as a slope of rise/run

4.  g [ % ] [ Pitch ] enters the value as a grade percentage, useful in construction and civil engineering

When solving for angle/pitch/slope/grade: repeated presses cycled through the four values: pitch (PTCH), angle (still labeled as PTCH), grade (labeled as %GRD), slope (labeled as SLP).

Examples

(1/16 fraction mode set)

Example 1:

Rise:  36 ft

Run:  45 ft

Results:

Diag: 57 ft 7 9/16 in 

[ Pitch ] key:

Pitch: 9 5/8 in

Angle: 38.66°

Grade: 80%

Slope: 0.8

Example 2:

Rise: 50 ft

Diagonal:  72.5 ft

Results:

Run: 52.5 ft

[ Pitch ] key:

Pitch: 11.42857 in

Angle: 43.60°

Grade: 95.2381%

Slope: 0.952381

Example 3:

Rise: 60 ft

Angle:  30°  (enter as 30 [ Pitch ] )

Results:

Run:  103 ft 11 1/16 in

Diag:  120 ft

[ Pitch ] key:

Pitch: 6 15/16 in

Angle: 30.00°

Grade: 57.73503%

Slope: 0.57735

Example 4:

Rise: 60 ft

Pitch: 4 in (enter as 4 [ Inch ] [ Pitch ])

Results:

Run:  180 ft

Diag:  189 ft 8 13/16 in

[ Pitch ] key:

Pitch: 4 in

Angle: 18.43°

Grade: 33.33333%

Slope: 0.333333

I hope you found this tip helpful,

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Calculated Industries Calculators: Memory Registers and Tape

Calculated Industries Calculators:  Memory Registers and Tape

Introduction

This post covers five Calculated Industries calculators:

Tradesman Calc - 4400

Construction Master 5 - 4050

Machinist Calc Pro - 4087

Pipe Trades Pro - 4095

ElectricCalc Pro - 5070

Memory Storage and Store Arithmetic

The calculators do not have storage arithmetic other than the independent memory register (M).   

Tradesman Calc - 4400	Construction Pro 5 - 4050	Machinist Calc Pro - 4087	Pipe Trades Pro - 4095	ElectricCalc Pro - 5070
M, registers 1 - 9	M only	M, registers 1 - 9	M, registers 1 - 9	M, registers 1 - 9
M+, M-	M+, M-	M+, M-	M+, M-	M+

Tape Memory

All the calculators listed except the ElectricCalc Pro has a tape listing memory.  The tape memory records all the arithmetic (+, -, x, ÷), percent (%), and parenthesis keystrokes.  For the square (x²) and square root (√), the numeric results are recorded.  The tape memory does not record any work involving any of the solver keys.

Tape Memory Controls

Clear the Tape:  [ On/C ] [ On/C ] (or do a Clear All)

Enter Tape Mode: [ Conv ] [ = ]

Scroll in Tape Mode: [ + ], [ - ]

Exit Tape Mode:  [ = ]

The table lists the number of steps can be stored:

Tradesman Calc - 4400	Construction Pro 5 - 4050	Machinist Calc Pro - 4087	Pipe Trades Pro - 4095
20	20	30	30

Sample Problems and Tape Memory

Problem 1:  1.99 x 50 + 100 =    (Result: 199.5)

All calculators return the same tape (spaces added for clarity):

01  1.99

02 x 50

03 + 100

TTL = 199.5

Problem 2:  4 1/2 in + 3 3/8 in =  (Result:  7 7/8 in)

All calculators return the same tape:

01   4 1/2 INCH

02 + 3 3/8 INCH

TTL = 7 7/8 INCH

Tape with arithmetic functions will work with units.

Problem 3:  ( 1.99 x 20 + 25 ) = + 10% =   (Result: 71.28)

Tradesman Calc (4400) tape:

01  ( 1.99

02  x 20

03  + ) 25

SUB = 64.8

05 +% 10

SUB % 71.28

TTL = 71.28

Pipe Trades Pro (4095) tape:

01  1.99    (first parenthesis is messing)

02  x 20

03  + ) 25

SUB = 64.8

05 +% 10

SUB % 71.28

TTL = 71.28

Construction Master 5 (4050) tape and 

Machinist Calc Pro (4087) tape:

The parenthesis are left out since neither of these calculators have parenthesis.  I have left the calculations in that order to ensure proper order of operations:

01  1.99    (first parenthesis is messing)

02  x 20

03  + 25

SUB = 64.8

05 +% 10

SUB % 71.28

TTL = 71.28

Problem 4:  15 x^2 x π  (Result:  706.85835)

All calculators return the same tape:

01 225   (shows 15^2)

02 x 3.141593

TTL = 706.85835

Problem 5:  24 x 59 = √   (Final Result:  √1416 = 37.62978)

All calculators return the same tape:

01 24

02 x 59 

TTL = 1416

The square root is totally ignored!

Problem 6:  24 √ x 59 √ =    (Result: 37.62978)

All calculators return the same tape...

01 4.898979 

02 x 7.681146

TTL = 37.62978

except the Trademsan Calc (4400) - sometimes:

01 24

02 x 7.681146

TTL = 37.62978   (this doesn't make sense!)

However, most of the time, I get the proper tape above.  This just a thing to watch out for.  

Note that √(24 * 59) = √24 * √59

Curious that none of the Calculator Industries finance and real estate calculators have the tape feature.  

The Recall Memory Feature:  Additional Calculations

The Recall Memory (Rcl) of the independent memory register returns three calculations:

TTL:  total or sum

AVG: average of all entries by M+

CNT:  count of all entries by M+

[ Rcl ] [ M+ ]: To display the contents of the independent register (total).

Keep pressing [ M+ ] to cycle through average, count, total.  Press [ On/C ] to exit.  

The notable exception is the ElectriCalc Pro:

[ Rcl ] [ 0 ]:  To display the contents of the independent register (total).

Keep pressing [ 0 ] to cycle through average, count, and total.  Press [ On/C ] to exit.  

Sample Data:

410, 359, 367, 388, 384

Recall memory M until it's cleared.  You can store 0 into Memory M or press RCL twice.  Insert presses of [ Conv ] when needed.  

410 M+

359 M+

367 M+

388 M+

384 M+

Note:  On the ElectriCalc Pro, press [ Stor ] [ M+ ] to use M+.

RCL M: 

TTL 1908  (TOTAL on the Machinist Calc Pro)

(Press M again)

AVG  381.6

(Press M again)

CNT  5   (COUNT on the Machinist Calc Pro)

(Press M again to cycle.)

That is a tour of the memory features on some of the industrial calculators from Calculated Industries.  Hope you find this useful!

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Construction Master 5: Area of Regular Polygons

Construction Master 5: Area of Regular Polygons

Introduction:  Area of a Regular Polygon

The area of a regular polygon is:

Area = 1/2 * P * A

where:
P = perimeter = n * S 
n = number of sides
S = side length
A = apothem length

Divided the regular polygon from drawing lines from the center to each of the polygon's vertices.  Triangles about the center are formed with a central angle, 360° ÷ n. 

The apothem bisects each of the triangles, with the angle nearest to the center of 180° ÷ n.   A right angle is formed between the side and apothem.   The small triangle formed has the base of the s ÷ 2 (since the apothem bisects the side) and A.  The triangle has angles half-central angle (HCA), 90°, and 180° - 90° - HCA.  I will refer to the third angle as the Pitch angle (see the diagram above). 

The trigonometric relationships are:

tan( Pitch ) = A / ( s / 2 )

A = s / 2 * tan(Pitch)

s = 2 * A / tan(Pitch)

It is possible to determine the area of regular polygon knowing the number of sides and either the side length or the apothem.

The Calculated Industries Construction Master 5 does not have trigonometric keys.  However, the Construction Master 5 has four keys that deal with right triangles:

[ Pitch ]:  angle in degrees.  Enter the angle as a unit-less measure.  For example, to enter 60°, press 60 [ Pitch ].  The angle considers the rise of the opposite side, and run the adjacent side.

[ Rise ]:  rise - opposite side.  The Rise is considered the apothem of length A.  You can enter either unit-less or measured amounts (feet/inches/yards/m). 

[ Run ]:  run - adjacent side.  You can enter either unit-less or measured amounts (feet/inches/yards/m).  This represents the side or half-side.

[ Diag ]:  hypotenuse.  The algorithms will not use this key in this blog. 

Known:  Number of Sides and Side Length

The Math:

Area

= 1/2 * P * A
= 1/2 * n * s * (s/2 * tan(Pitch))
= 1/4 * n *  (s * tan(Pitch))

Keystrokes:

180 [ ÷ ] n [ Conv ] (+/-) [ + ] 90 [ Pitch ]
s [ Run ]
[ Rise ] [ × ] [ Rcl ] [ Run ] [ × ] n [ ÷ ] 4 [ = ]

Example:
s = 40 ft, n = 6

180 [ ÷ ] 6 [ Conv ] (+/-) [ + ] 90 [ Pitch ]    (Display:  PTCH 60.00°)
40 [ Feet ] [ Run ]
[ Rise ] [ × ] [ Rcl ] [ Run ] [ × ] 6 [ ÷ ] 4 [ = ]   (Display:  4156.922 SQ FEET)

Area ≈ 4156.922 ft^2

Known:  Number of Sides and Apothem

The Math

Area

= 1/2 * P * A
= 1/2 * (n * s) * A
= 1/2 * n * (2 * A) / tan(Pitch) * A
= n * A  * (A / tan(Pitch))

Keystrokes:

180 [ ÷ ] n [ Conv ] (+/-) [ + ] 90 [ Pitch ]
s [ Rise ]
[ Run ] [ × ] [ Rcl ] [ Rise ] [ × ] n [ = ]

Example:
A = 40 ft, n = 6

180 [ ÷ ] 6 [ Conv ] (+/-) [ + ] 90 [ Pitch ]   (Display:  PTCH 60.00°)
40 [ Feet ] [ Rise ]
[ Run ] [ × ] [ Rcl ] [ Rise ] [ × ] 6 [ = ]   (Display:  5542.563 SQ FEET)

Area ≈ 5542.563 ft^2

And that is how to find the area of a regular polygon using the Construction Master 5.

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Construction Master 5: Right Triangles

Construction Master 5:   Right Triangles

Introduction

The Calculated Industries Construction Master 5 does not have trigonometric keys, but it has four keys to dedicated to solving problems with right triangles, which appear a lot in construction.  Those four keys are:

[ Pitch ]:  there are several ways to enter the pitch:

If the amount is in inches, then the measurement is put as a pitch (x inches per 12 inches).  Example:  3 [ Inch ] [ Pitch]  inputs the angle as a 3 inch pitch (approximately 14.04°)

If the amount is in percent, the angle is entered as a percent grade.   Example: To enter 2% grade, press 2 [ % ] [ Pitch ] (approximately 1.15°)

If the amount is not attached to a unit, the amount is entered as degrees.  Example: To enter 30°, press 30 [ Pitch ].

[ Rise ]:  rise - opposite side.  Amounts can be entered with or without units.   

[ Run ]:  run - adjacent side.  Amounts can be entered with or without units.

[ Diag ]:  diagonal - hypotenuse.  Amounts can be entered with or without units.  Solving for the diagonal is known as a squaring-up calculation. 

To solve for a variable, just press the key without entering an amount. 

After all the variables have been calculated, you can calculate perimeter and area by:

Perimeter:  [ Rcl ] [ Rise ] [ + ] [ Rcl ] [ Run ] [ + ] [ Rcl ] [ Diag ]

Area:  [ Rcl ] [ Rise ] [ × ] [ Rcl ] [ Run ] [ ÷ ] 2

Examples 

Example 1:

Given:  Diagonal:  17.4 feet, Pitch:  20°

Results:
Rise:  5.95115 feet;  Run:  16.35065
Perimeter:  39.7018 feet;  Area:  48.65259 square feet

Example 2:

Given: Rise:  50 feet, Run:  40 feet

Results:
Diagonal:  64 feet 3/8 inch;  Pitch:  51.34°
Perimeter:  154 feet 3/8 inch feet;  Area:  1000 square feet

Example 3:

Given:  Grade: 3%, Feet: 17.5 Feet

Note, to enter the grade:  3 [ % ] [ Pitch ]

Results:
Run:  583.3333 ft, Diag:  583.5958 ft
Angle:  1.72°
Perimeter:  1184.429; Area: 5104.167 square feet

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

TI-84 Plus: Staircases

TI-84 Plus:  Staircases

  

Given the rise (height from lower floor to upper floor), run (length of the staircase), and desired riser height (how high each stair is), the program STAIRS calculates the number risers needed, along with the width of each stair, the incline, and finally illustrates the staircase. STAIRS is designed with inches and feet (US units) in mind. 

Formulas

Given:  Rise, Run, Desired Rise Height (DRH)

Number of Risers:

n = rise/DRH, rounded to the nearest integer

Tread width:

TW = run/(n – 1)

Adjusted Riser Height (ARH)

ARH = rise/n, rounded to the nearest 1/16^th

One way to approach this: 

ARH = round(16*frac(rise/n),0)*16 + int(rise/n)

Incline:

θ = atan(RH/TW)

Other Calculations:

Stringer:

S = (n – 1)*√(ARH^2 + TW^2)

Number of Stairs:

N_stairs = n - 1

TI-84 Plus Program: STAIRS

Input:  Rise, Run, Desired Riser Height.  Keep the units consistent.  (12 inches = 1 foot)

Output:  Number of Risers (R), Tread width of each stair (T), Adjusted Riser Height (H), Angle of Incline (θ)

* Adjusted Riser Height is rounded to the nearest 1/16^th (of an inch).  This is accomplished by the line iPart(H)+round(16*fPart(H),0)/16. 

The graph screen shows the staircase.  A stat plot shows where each stair ends with X (L1) representing the position and Y representing the height (L2). 

The program sets the TI-84 Plus to Degrees mode.

"EWS 2016-12-03"

Degree

Input "RISE:",B

Input "RUN:",A

Input "DESIRED RISER HEIGHT:",H

round(B/H,0)→N

A/(N-1)→T

B/N→H

"ROUND H TO 1/16"

iPart(H)+round(16*fPart(H),0)/16→H

tan^-1(H/T)→θ

√(H²+T²)*(N-1)→S

Disp "NUMBER OF RISERS:",N

Disp "TREAD WIDTH:",T

Pause

Disp "ADJ. RISER HEIGHT:",H

Disp "ANGLE:",θ

Pause

{0}→L1:{0}→L2

­.5→Xmin:A+.5→Xmax

­.5→Ymin:B+.5→Ymax

ClrDraw

For(I,1,N-1)

augment(L1,{I*T})→L1

augment(L2,{I*H})→L2

End

PlotsOff

PlotsOn 1

Plot1(xyLine,L1,L2)

Line(0,0,A,0)

Line(A,0,A,B)

For(I,0,N-1)

Line(T*I,H*I,T*I,H*(I+1))

Line(T*I,H*(I+1),T*(I+1),H*(I+1))

End

DispGraph

Examples

All amounts are in inches.

Example 1:  Rise = 35 in, Run = 84 in, Desired Riser Height = 7 in

Results:  Number of Risers: 5, Tread width: 21 in, Adjusted Riser Height:  7 in, θ ≈ 18.43495°

Example 1 is shown in the screen shots above.

Example 2:  Rise = 40 in, Run = 90 in, Desired Riser Height = 7 in

Results:  Number of Risers: 6, Tread width: 18 in, Adjusted Riser Height:  6.6875 in,

θ ≈ 20.38143°

Example 3:  Rise = 56 in, Run = 50 in, Desired Riser Height = 6.5 in

Results:  Number of Risers: 9, Tread width: 6.25 in, Adjusted Riser Height:  6.25 in,

θ ≈ 45°

This program was inspired by the Calculated Industries Construction Master 5 calculator

Eddie

This blog is property of Edward Shore, 2016

TI-84 Plus: Rake Wall

TI-84 Plus:  Rake Wall

The program RAKEWALL calculates:

*  The positions and lengths of studs on a rake wall

*  Angle of the incline

Adding Illustration

I wanted to do something different and present an illustration rather than just text answers.  What is nice of the TI-84 Plus (and really the TI-8x family extending back to the TI-81) is that the programming language allowing for easy transition between modes (home, graphing, matrix editing, table, etc.).  With RAKEWALL, I not only display text answers, but a visual of how the rake wall is laid out. 

Sometimes the best way to present information is through visuals, not just text.  I want to further explore this whenever it is warranted.

TI-84 Plus Program RAKEWALL

Input:  Rise, Run, O.C. (on center spacing).   RAKEWALL does not specify units, keep that in mind.  Use consistent units.  As a reminder, 12 inches is 1 foot.

Output:  Angle (in Degrees), stud spacing stored in list L1, stud lengths stored in list L2.  The program ends on the graph screen.  Press [ trace ] to see the values.  X is the length from the where the incline and base meet to the stud, Y is the stud length.

Please note that results are exact and not rounded (i.e. to the nearest 1/16^th).

Program:

"EWS 2016-12-01"

ClrDraw

Degree

Input "RUN:",L

Input "O.C. SPACING:",S

Input "BASE:",B

Input "RISE:",R

seq(X,X,L,0,­-S)→L1

tan^-1(R/L)→θ

L1*tan(θ)+B→L2

augment(L1,{0})→L1

augment(L2,{B})→L2

Disp "ANGLE:",θ

Disp "NUMBER OF STUDS:",dim(L1)-2

Disp "(L1: DIST. FROM SHORT PT."

Disp "L2: STUD LENGTH)"

Pause

PlotsOff

PlotsOn 1

Plot1(xyLine,L1,L2)

­0.5→Ymin

B+R+.5→Ymax

­.5→Xmin

L+.5→Xmax

For(I,1,dim(L1))

Line(L1(I),0,L1(I),L2(I))

End

Line(0,0,L,0)

Line(L,0,L,B)

DispGraph

Example:

Run:  6 feet

O.C.:  1 foot 6 inches, or 16/12 inches

Base:  6 feet

Rise:  5 feet

This program was inspired by the Calculated Industries Construction Master 5 calculator.  I am thinking about purchasing their Construction Pro calculator (most likely the app). 

Happy December!

Eddie

This blog is property of Edward Shore, 2016.

My Calculated Industries Calculator Collection

The company Calculated Industries (http://www.calculated.com/) manufactures specialized calculators.

Here is my small collection:

Machinist Calc Pro

I bought this calculator today at a pawn shop in Pomona. It came with the box, instructions, and the calculator in an Armadillo Gear case. I never seen a calculator being in such an industrial case before. This calculator is specialized in machinery calculations with a built in tables of drill points, drill sizes, and thread sizes. Trigonometric functions are featured (Adj, Opp, Hyp, Angle for right triangles and Sine, Cosine, Tangent for general trigonometry).

The manual is a good size book and as of today I have yet to go through it and do the examples.

Qualifier Plus IIx

This calculator specializes in real estate calculations, which include finding qualified amounts, time value of money, and PITI (principal, interest, taxes, & interest). I picked up this calculator at another pawn shop in Pomona, which is sadly no longer there.

The next three calculators deal with construction.

ProjectCalc Plus

I think I got all three of construction calculators from Home Depot throughout last year.

First is the simple calculator. The calculator had built in tables for concrete, carpet, and tile sizes (and more).

Material Estimator

To me, the Material Estimator is the big cousin of the ProjectCalc Plus. The Material Estimator has all the features plus an electric tape to keep track of calculations, a hard cover that stores the manual (which is really neat), and it is solar and battery powered.

Construction Master 5

The Construction Master takes a different specialty than the ProjectCalc and Material Estimator. The Construction Master focuses on stairs, roofs, risers, and walls. Like the Material Estimator, the Construction Master has an electric tape and the manual is stored in the calculator's case.

What is common for all the construction calculators and the Machinist Calc is that we can make calculations using yards-feet-inch, meters-centimeters-millimeters calculations and conversions. This is a super feature.

I really could use some more time learning the features of these calculators. So there is my collection.

Eddie


This blog is property of Edward Shore. 2013