Matt measures the angle of elevation of the peak of a mountain as 35 degrees. Susie, who is 1200 feet closer on a straight level path, measures the angle of elevation as 42 degrees. What is the distance from Matt to the peak of the mountain?

Question

(Use law of Sines, AAS)

Answer 1

Let x be the distance from Matt to the peak of the mountain.

Using the Law of Sines, we have:

sin(35°) / x = sin(42°) / (x - 1200)

Solving for x, we get:

x = (1200 * sin(35°)) / (sin(42°) - sin(35°))

x ≈ 1645.7 feet