Question

Two observers simultaneously see an airplane overhead and between them. They measure

their angle of elevation to the airplane and obtain 48° and 73º. The airplane is 1.7 miles
directly above the point shown in the figure below. How far are the two observers from each
other? Round your answer to the nearest hundreth of a mile.

Answer 1

2.05 mi

Explanation:

I don't see a figure, so I am guessing that the plane is 1.7 miles above the ground.

Let x = distance of observer 1 from that point

y = distance of observer 2 from that point

Tan 48 = 1.7/x and tan 73 = 1.7/y

x tan 48 = 1.7 y tan 73 = 1.7

x = 1.7/tan 48 y = 1.7/tan 73

x + y = distance between the observers

x + y = 1.7/tan 48 + 1.7/tan 73

= 2.05 mi