take a triangle ABC such that left vertex is A, right vertex is C and centre top is B. angle A is theta , angle C is alpha, side AB is "r". now draw a line from vertex A towards line BC. such that it meets BC at D. angle BAD is beta. now i have to know what is the value of AD in terms of alpha, beta , theta and "r".
-
Start by filling in the angles, using the fact that the angles of a triangle sum to 180.
Angle B = 180 - θ - α
Angle ADB = θ + α - β
Then use the law of sines to relate lengths and angles within triangle ABD.
sin(ADB) / r = sin(B) / AD
Solve for the length AD.
AD = sin(180 - θ - α) / sin( θ + α - β) * r
Angle B = 180 - θ - α
Angle ADB = θ + α - β
Then use the law of sines to relate lengths and angles within triangle ABD.
sin(ADB) / r = sin(B) / AD
Solve for the length AD.
AD = sin(180 - θ - α) / sin( θ + α - β) * r