Question

An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1950 feet

apart. As the airplane passes over the line joining them, each observer takes a
sighting of the angle of elevation to the plane, as indicated in the figure. If A = 45°,
and B = 40°, how high is the airplane?
h
B)
L
The elevation of the plane is approximately feet.
(Do not round until the final answer. Then round to two decimal places as needed.)

Answer 1

889.70 feets

Explanation:

From the solution diagram attached :

C = 180 - (40 + 45) = 95°

According to the sine rule :

Sin95 / 1950 = Sin40 / b = Sin 45 / a

1950 sin40 / sin 95 = b = 1248.22 ft

1950 sin 45 / sin 95 = a = 1384.13 ft

Sin 40 = h / 1384.13

h = 1384.13 * sin 40

h = 889.70 feets