Question

A blimp is 1600 meters high in the air and measures the angles of depression to two stadiums to the east of the blimp. If those measurements are 71.7° and 25.2°, how far apart are the two stadiums?

A. 3929 m
B. 3327 m
C. 3150 m
D. 2871 m

Answer 1

The explanation of the problem is as shown in the figure.
A blimp ⇒⇒⇒ point A
stadium 1 ⇒⇒⇒ point B
stadium 2 ⇒⇒⇒ point C
height of the blimp ⇒⇒⇒ AD = 1600
depression angle of stadium 1 ⇒⇒⇒ ∠y = 71.7°
depression angle of stadium 2 ⇒⇒⇒ ∠x = 25.2°
distance between the two stadiums ⇒⇒⇒ d

DC = AD * tan (90° - x) = 1600 * tan( 90° - 25.2° )
DB = AD * tan (90° - y) = 1600 * tan( 90° - 71.7° )

∴ d = DC - DB
= 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]
= 2,871 meters

∴ The correct choice is option (D)