Question

The height of the Eiffel Tower is 1050 feet. From the top, the angle of depression to a soccer ball on the ground is 20 degrees. Find, to the nearest foot, the distance from the soccer ball to the base of the Eiffel Tower.

Answer 1

Since the angle of depression from the Eiffel tower is congruent to the angle of elevation from the soccer ball, the angle of elevation from the soccer field is 20°

Now, we can use the trigonometric function tangent to find the distance from the soccer ball to the base of the Eiffel Tower:
$tan( \alpha )= \frac{opposite.side}{adjacent.side}$
$tan(20)= \frac{1050}{a}$
$a= \frac{1050}{tan(20)}$
$a=2884.85$

We can conclude that the distance from the soccer ball to the base of the Eiffel Tower is 2884.85 feet.