SOLUTION: A small aircraft pilot flying towards two mountains in foggy conditions wants to map its position in comparison to two control towers. They discover the aircraft is on a true beari

Question 1203414: A small aircraft pilot flying towards two mountains in foggy conditions wants to map its position in comparison to two control towers. They discover the aircraft is on a true bearing of 143 degrees from tower A and on a true bearing of 075 degrees from tower B. Tower A is 25km north of tower B.
Determine the distance from the aircraft to each tower.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A small aircraft pilot flying towards two mountains in foggy conditions wants to map its position in comparison to two control towers. They discover the aircraft is on a true bearing of 143 degrees from tower A and on a true bearing of 075 degrees from tower B. Tower A is 25km north of tower B.
Determine the distance from the aircraft to each tower.
=========================
Use P for the position of the plane, and A, B & P for the angles, and side a is opposite angle A, etc.
---
Angle A = 37 degs (180 - 143)
Angle B = 75 degs
Angle P = 68 degs (180 - (A + B))
Side p = 25 km
Use the Law of Sines to find sides a & b
---
a/sin(A) = p/sin(P)
a = 25*sin(37)/sin(68)
a = ~ 16.227 km, the distance to tower B
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b/sin(B) = p/sin(P)
b = 25*sin(75)/sin(68)
b = ~ 26.045 km. the distance to tower A

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