Question

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 3º. How far away is Gateway Arch, to the nearest tenth of a mile?

Answer 1

d = 12,021.1 ft

The Gateway Arch is 12,021.1 ft away

Explanation:

Given;

Angle of elevation = 3°

Height of arch = 630 ft

Tanθ = opposite/adjacent

Opposite = 630 ft

Adjacent = d

Substituting the values;

Tan3 = 630/d

d = 630/tan3

d = 12,021.1 ft

The Gateway Arch is 12,021.1 ft away

Answer 2

`x = 12021.1\,ft\,(2.3\,mi)`

Explanation:

The distance is given by the following trigonometric equation:

`x = (y)/(\tan \alpha)`

`x = (630\,ft)/(\tan 3^(\textdegree))`

`x = 12021.1\,ft\,(2.3\,mi)`