Question

Two airplanes flying 1.0 km apart at the same altitude spot a target ahead of them on the ground. The angles of depression subtended by the target at the two airplanes are 45o and 37o. The airplanes and the target are in the same vertical plane. What is the altitude (in meters) at which the planes are flying? (Note: For the distances involved, the earth can be considered as flat.)
a. 2900
b. 3060
c. 1000
d. 2000

Answer 1

Answer:

option B

Explanation:

given,

two plane are moving in same altitude at a distance of 1.0 km apart.

angle of depression of the two planes given are 45° and 37°

now, the diagram is attached below

using diagram,

now in ΔAOC

tan 45° = $\dfrac{h}{x}$

x = h..................(1)

now using triangle ΔBOD

tan 37° = $\dfrac{h}{x + 1000}$

from equation (1)

0.754 =  $\dfrac{h}{h + 1000}$

0.754 h + 753.56 = h

0.246 h = 753.56

h = 3063.5 m

hence, the correct answer is option B