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Sherry spots a car as she is looking down at a 70° from the top of the Eiffel Tower, which is 1063 ft tall. How far away from the base of the tower is the car? Round to the nearest hundredth.

A) 536.23 ft
B) 533.45 ft
C) 333.97 ft
D) 349.12 ft

User Valerion
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1 Answer

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Final answer:

By using the tangent of the angle of depression from the Eiffel Tower, we calculate the base distance from the tower to a car to be approximately 333.97 feet, making the right option (C) 333.97 ft.

Step-by-step explanation:

To determine how far away the car is from the base of the Eiffel Tower, we need to apply trigonometric principles. We are given that Sherry looks down from the top of the Eiffel Tower at an angle of 70° and that the height of the tower is 1063 feet. We will use the tangent function, which relates the angle of depression with the opposite side (height of the tower) and the adjacent side (distance from the base of the tower to the car).

The tangent of the angle is equal to the opposite side divided by the adjacent side: tan(70°) = opposite/adjacent, which is tan(70°) = 1063 feet / distance to car. To find the distance to the car, we rearrange this to: distance to car = 1063 feet / tan(70°).

After calculating, we get: distance to car ≈ 333.97 feet. Therefore, the correct answer is (C) 333.97 ft, rounded to the nearest hundredth.

User Rzymek
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