A traveler is driving across the country and spots Gateway Arch in St. Louis, Missouri. She has read that the arch is 630 feet tall. Her angle of

elevation to the top of the arch is 30. How far away is Gateway Arch, to the nearest tenth of a mile?

The answer is 0.2mile

Step-by-step explanation:

The vertical height of the building, which is 630ft, is opposite the angle of elevation (30°).

While the horizontal distance to the tower is adjacent to the building. So, we take the tangent of the angle of elevation in terms of this unknown distance (x) and the vertical height.

So,

Tangent = opposite : adjacent

Tan30° = 630ft : x

x = 630ft : tan30°

x = 1091.192ft

But,

1 mile = 5,280ft

1091.192ft = (1/5280) x 1091.192

= 0.2mile