HP Prime and TI-84 Plus: Forward Intersection
Introduction
The program
FORDINT calculates the third point on a triangle where the coordinates of
points A (xa, xb) and B (xb, yb) are
known. Also, a line towards P point is
aimed from point A at angle α° and from point B at angle β°. See the diagram below.
Formulas:
Output is point
P:
xp = (xa cot β +
xb cot α + (yb – ya))/(cot α + cot β)
yp = (ya cot β +
yb cot α + (xa - xb))/(cot α + cot β)
γ = 180° - α - β
cot θ = 1/tan θ
Note that
FORDINT will set the calculator to Degrees mode.
HP Prime Program FORDINT
Input: xa, ya, α, xb, yb, β
Output: 3 element list: {xp, yp, γ} and Degrees mode is set
EXPORT
FORDINT(xa,ya,a,xb,yb,b)
BEGIN
// Forward Intersection
// 2016-11-16 EWS
LOCAL xp,yp,c;
// Degree Mode
HAngle:=1;
// Calculation
xp:=(xa*COT(b)+xb*COT(a)+(yb-ya))
/(COT(a)+COT(b));
yp:=(ya*COT(b)+yb*COT(a)+(xa-xb))
/(COT(a)+COT(b));
c:=180-a-b;
RETURN {xp,yp,c};
END;
TI-84 Plus Program: FORDINT
Input: Variables are prompted
Output: Results are displayed
|
Variable
|
TI-84
Plus Variable
|
Variable
|
TI-84
Plus Variable
|
Variable
|
TI-84
Plus Variable
|
|
xa
|
N
|
ya
|
S
|
α
|
A
|
|
xb
|
O
|
yb
|
T
|
β
|
B
|
|
xp
|
P
|
yc
|
U
|
γ
|
C
|
"FORWARD
INTERSECT"
"2016-11-16
EWS"
Degree
Input "XA:
",N
Input "YA:
",S
Input "θA:
",A
Input "XB:
",O
Input "YB:
",T
Input "θB:
",B
(N/tan(B)+O/tan(A)+(T-S))/(1/(tan(A))+1/(tan(B)))→P
(S/tan(B)+T/tan(A)+(N-O))/(1/(tan(A))+1/(tan(B)))→U
180-A-B→C
Disp "XP:
",P
Disp "YP:
",U
Disp "θC:
",C
Example:
Point A: (1000, 950), angle towards point P: 30°
Point B: (1012, 997), angle towards point P: 44°
Result:
Point P: (approximately) (1024.49237, 975.078358)
Angle γ: 106°
Source: Casio. Casio
fx-FD10 Pro User’s Guide Tokyo. 2014
This blog is
property of Edward Shore, 2016.