Two observers, in the same vertical plane as a kite and 30 feet apart, observe the kite at angles of 62° 𝑎𝑛𝑑 78°, as shown below. Find the height of the kite, to the nearest foot

Answer 1

Let x be the distance the a point directly under the kite and the second observer.

The distance from the first observer to the point under the kite is 30+x. Let y be the height of the kite.

tan(62°) = y/(30+x) --> y = (30+x)tan(62°)

tan(78°) = y/x --> x = y/tan(78°)

y = (30 + y/tan(78°)tan(62°)

y = 30tan(62°)/(1-tan(62°)/tan(78°)) = 94 feet