Finding Third Coordinate Of a Triangle - c

Question

i have an assignment for Programming class.
i have finished 80 percent of it, i am not able to complete the last part.
We have to find the distance between the shore and the boat(Point C) And Coordinates Of The Boat (Point C).
We are given (X,Y) coordinates And Angles of Points A and B.
Given A(76,316) B(57,516) Angle A = 17° and B = 17° Angle.
So Far i found AB= 200.9 AC= 105.04 BC = 105.04 C = 146° And the distance between the shore and the boat d = 30.71.
I tried everything but i am not able to find the Coordinates of Point C (Boat).
The Output is also Given : d = 30.71, Coordinates of C = C(97.07,418.90)
Please help me to find coordinates of Point C.
#include <stdio.h>
#include <math.h>
float radian(int degree);
float get_watchtowers_distance(int x1,int y1,int x2,int y2);
float get_boat_distance(float d,int alpha,int beta);
int main(){
get_watchtowers_distance(76,316,57,516);
get_boat_distance(200.90,17,17);
}
float radian(int degree){
return degree * (M_PI/180);
}
float get_watchtowers_distance(int x1,int y1,int x2,int y2){
return sqrtf(powf(x2-x1,2.0f)+powf(y2-y1,2.0f));
}
float get_boat_distance(float d,int alpha,int beta){
float a,b,c = 180 - (float)alpha - (float)beta;
a = (float)radian(alpha);
b = (float)radian(beta);
c = (float)radian(c);
printf("%.2f %.2f %.2f\n",a,b,c);
float B,A = d*sinf(a)/sinf(c);
B = d*sinf(b)/sinf(c);
float dist,area = 1.0f/2.0f*A*B*sinf(c);
dist = 2*area/d;
printf("AC Distance : %.2f , BC distance : %.2f\n",A,B);
printf("Boat Distance : %.2f\n", dist);
return dist;
}

Answer 1

Simpler approach to find d distance. We can express lengths of the left and right parts of base through d and cotangents
aa = d * ctg(alpha)
bb = d * ctg(beta)
aa + bb = l
d * (ctg(alpha) + ctg(beta)) = l
d = l / (ctg(alpha) + ctg(beta)) =
= l * sin(alpha) * sin(beta) / sin(alpha+beta)
Now you can find C coordinates using normalized vector ab and perpendicular component
abx = (b.x - a.x) / l
aby = (b.y - a.y) / l
aalen = d / tg(alpha)
c.x = a.x + abx * aalen - aby * d
c.y = a.y + aby * aalen + abx * d

Answer 2

There you go I have written some code for your question..
float get_coordinates(int x1, int y1, int x2, int y2, float alpha, float beta){
float a_angle_alpha, b_angle_beta, c_angle_delta;
c_angle_delta = 180 - (float)alpha - (float)beta;
printf("Alpha Angle in Degrees = %.2f\nBeta Angle in Degrees = %.2f\nDelta Angle in Degrees = %.2f\n", alpha, beta, c_angle_delta);
a_angle_alpha = (float)radian(alpha);
b_angle_beta = (float)radian(beta);
c_angle_delta = (float)radian(c_angle_delta);
printf("Alpha in radiance: %.2f\nBeta in radiance: %.2f\nDelta in radiance: %.2f\n", a_angle_alpha, b_angle_beta, c_angle_delta);
int u, v;
float d;
u = x2 - x1;
v = y2 -y1;
printf("u = %.d\nv = %.d\n", u, v);
float d1_distance_AB, d2_distance_BC, d3_distance_AC;
d1_distance_AB = sqrtf((u*u)+ (v*v));
d2_distance_BC = d1_distance_AB*sinf(b_angle_beta)/sinf(c_angle_delta);
d3_distance_AC = d1_distance_AB*sinf(a_angle_alpha)/sinf(c_angle_delta);
printf("Distance between A and B: %.2f\nDistance between B and C: %.2f\nDistance between A and C: %.2f\n",d1_distance_AB, d2_distance_BC, d3_distance_AC);
float RHS1, RHS2;
float x3, y3;
RHS1 = ((x1 * u) + (y1 * v) + (d2_distance_BC * d1_distance_AB * cosf(a_angle_alpha)));
RHS2 = ((y2 * u) - (x2 * v) - (d2_distance_BC * d1_distance_AB * sinf(a_angle_alpha)));
x3 = ((1 / (d1_distance_AB * d1_distance_AB)) * ((u * RHS1) - (v * RHS2)));
y3 = ((1 / (d1_distance_AB * d1_distance_AB)) * ((v * RHS1) + (u * RHS2)));
printf("Coordinates of Boat at point C is = %.2f:%.2f (x:y)", x3, y3);
float coordinates[2] = {x3,y3};
return coordinates;
}
Full Code:
#include <stdio.h>
#include <math.h>
float radian(int degree);
float get_watchtowers_distance(int x1,int y1,int x2,int y2);
float get_boat_distance(float d,int alpha,int beta);
float get_coordinates(int x1, int y1, int x2, int y2, float alpha, float beta);
int main(){
get_watchtowers_distance(76,316,57,516);
get_boat_distance(200.90,17,17);
get_coordinates(76,316,57,516,17,17);
}
float radian(int degree){
return degree * (M_PI/180);
}
float get_watchtowers_distance(int x1,int y1,int x2,int y2){
return sqrtf(powf(x2-x1,2.0f)+powf(y2-y1,2.0f));
}
float get_boat_distance(float d,int alpha,int beta){
float a,b,c = 180 - (float)alpha - (float)beta;
a = (float)radian(alpha);
b = (float)radian(beta);
c = (float)radian(c);
printf("%.2f %.2f %.2f\n", a, b, c);
float B,A = d*sinf(a)/sinf(c);
B = d*sinf(b)/sinf(c);
float dist,area = 1.0f/2.0f*A*B*sinf(c);
dist = 2*area/d;
printf("AC Distance : %.2f , BC distance : %.2f\n",A,B);
printf("Boat Distance : %.2f\n", dist);
return dist;
}
float get_coordinates(int x1, int y1, int x2, int y2, float alpha, float beta){
float a_angle_alpha, b_angle_beta, c_angle_delta;
c_angle_delta = 180 - (float)alpha - (float)beta;
printf("Alpha Angle in Degrees = %.2f\nBeta Angle in Degrees = %.2f\nDelta Angle in Degrees = %.2f\n", alpha, beta, c_angle_delta);
a_angle_alpha = (float)radian(alpha);
b_angle_beta = (float)radian(beta);
c_angle_delta = (float)radian(c_angle_delta);
printf("Alpha in radiance: %.2f\nBeta in radiance: %.2f\nDelta in radiance: %.2f\n", a_angle_alpha, b_angle_beta, c_angle_delta);
int u, v;
float d;
u = x2 - x1;
v = y2 -y1;
printf("u = %.d\nv = %.d\n", u, v);
float d1_distance_AB, d2_distance_BC, d3_distance_AC;
d1_distance_AB = sqrtf((u*u)+ (v*v));
d2_distance_BC = d1_distance_AB*sinf(b_angle_beta)/sinf(c_angle_delta);
d3_distance_AC = d1_distance_AB*sinf(a_angle_alpha)/sinf(c_angle_delta);
printf("Distance between A and B: %.2f\nDistance between B and C: %.2f\nDistance between A and C: %.2f\n",d1_distance_AB, d2_distance_BC, d3_distance_AC);
float RHS1, RHS2;
float x3, y3;
RHS1 = ((x1 * u) + (y1 * v) + (d2_distance_BC * d1_distance_AB * cosf(a_angle_alpha)));
RHS2 = ((y2 * u) - (x2 * v) - (d2_distance_BC * d1_distance_AB * sinf(a_angle_alpha)));
x3 = ((1 / (d1_distance_AB * d1_distance_AB)) * ((u * RHS1) - (v * RHS2)));
y3 = ((1 / (d1_distance_AB * d1_distance_AB)) * ((v * RHS1) + (u * RHS2)));
printf("Coordinates of Boat at point C is = %.2f:%.2f (x:y)", x3, y3);
float coordinates[2] = {x3,y3};
return coordinates;
}
Output:
0.30 0.30 2.55
AC Distance : 105.04 , BC distance : 105.04
Boat Distance : 30.71
Alpha Angle in Degrees = 17.00
Beta Angle in Degrees = 17.00
Delta Angle in Degrees = 146.00
u = -19
v = 200
Distance between A and B: 200.90
Distance between B and C: 105.04
Distance between A and C: 105.04
Coordinates of Boat at point C is = 97.07:418.90 (x:y)

Answer 3

To find the distance d directly without determining point C, first, you can calculate the area S of the triangle in two ways.
S = 0.5 * l * d
S = 0.5 * l * l * sin(a) * sin(b) / sin(a + b)
Equating the two and canceling out 0.5 * l gives d = l * sin(a) * sin(b) / sin(a + b).