a cable car carries passengers from a point A

Question

a cable car carries passengers from a point A, which is 1.2 miles from a point B at the base of a mountain, to a point P at the top of the mountain. The angles of elevation of P from A and B are 𝛼 = 24° and 𝛽 = 75°, respectively. (Round your answers to one decimal place.)

(a)  Approximate the distance between A and P. mi=?

(b) Approximate the height of the mountain. mi= ?

Answer 1

Draw and label a diagram!

m∠A = 24°

m∠APB = 48°

m∠PBA = 105°

Drop a perpendicular from P to the base, C

m∠PCB = 75°

AB = 1.2 mi or 6336 ft

Use Law of Sines toe determine AP and PC