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
Accepted Solution
A:
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