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

Question

Allison Allen · Accepted Answer

#color(indigo)("Distance between the car and base of Eiffel tower is " = 386.9'#

#hat DAC = hat ACB = 70^@, Ab = h = 1063', " To find " BC#

#tan hat(ACB) = (AB) / (BC) = h / (BC)#

#bar (BC) = h / tan hat(ACB) = 1063 / tan 70#

#color(indigo)("Distance between the car and base of Eiffel tower" = BC = 386.9'#

Caroline Aucoin · Answer

undefined To find the distance from the base of the tower to the car, we can use trigonometry. The tangent function relates the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the tower, and the adjacent side is the distance from the base of the tower to the car. We can set up the equation as follows:

$$ \tan(70^\circ) = \frac{\text{height of tower}}{\text{distance to the car}} $$

Solving for the distance to the car:

$$ \text{Distance to car} = \frac{\text{height of tower}}{\tan(70^\circ)} $$

Substituting the given values:

$$ \text{Distance to car} = \frac{1063 \, \text{ft}}{\tan(70^\circ)} $$

Using a calculator:

$$ \text{Distance to car} \approx \frac{1063}{\tan(70^\circ)} \approx \frac{1063}{2.7475} \approx 387.08 \, \text{ft} $$

So, the car is approximately 387.08 feet away from the base of the Eiffel Tower.