Question #104451
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.
1
Expert's answer
2020-03-04T18:03:25-0500



Let L denote a  blimp, A and B - cars. Then LR=2460LR = 2460  feet , φ1=26.5°,φ2=34.9°.\varphi_1 = 26.5°, \varphi_2 = 34.9°. The goal is to find distance AB=AR+RB.AB = AR + RB.\\

From the triangle ALRALR : AR=LRtan(90°φ1)24602=4920AR = LR\cdot \tan(90°-\varphi_1) \approx 2460\cdot 2=4920\\

From the triangle BLRBLR : RB=LRtan(90°φ2)24601.433526.3RB = LR\cdot \tan(90°-\varphi_2) \approx 2460\cdot1.43\approx3526.3\\

Finaly, AB=AR+RB=4920+3526.38446.38446.AB = AR + RB = 4920+3526.3 \approx 8446.3 \approx 8446.\\

Answer: The parked cars are 8446 feet apart.



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Comments

Assignment Expert
03.03.20, 12:35

Dear visitor. Please use the panel for submitting new questions.

Antoni Perez
03.03.20, 04:43

and observer standing on a cliff 320 feet above the ocean measures angles of depression of the near and far side of the island to be 16.5° and 10.5° respectively how long is the island to the nearest foot

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