Answer to Question #104451 in Trigonometry for Antoni Perez

Question

13. A blimp is flying parallel to a road and is 2460 feet directly above it. The angles of depression of two parked cars on the road are 34.9° and 26.5°. TO the nearest foot, how far apart are the parked cars? (Note: The blimp is above a line between the parked cars.

Answer 1

Let L denote a  blimp, A and B - cars. Then $LR = 2460$  feet , $\varphi_1 = 26.5°, \varphi_2 = 34.9°.$ The goal is to find distance $AB = AR + RB.\\$

From the triangle $ALR$ : $AR = LR\cdot \tan(90°-\varphi_1) \approx 2460\cdot 2=4920\\$

From the triangle $BLR$ : $RB = LR\cdot \tan(90°-\varphi_2) \approx 2460\cdot1.43\approx3526.3\\$

Finaly, $AB = AR + RB = 4920+3526.3 \approx 8446.3 \approx 8446.\\$

Answer: The parked cars are 8446 feet apart.