Question

A tourist standing on the New York City coast sees the Statue of Liberty, which is 305 feet tall. She must tilt her head 9 degrees upwards to look at its head. How far away is she from the base of the statue? Round your answer to the nearest whole foot.

Answer 1

Given:

Height of the Statue of Liberty = 305 feet

Angle of elevation = 9 degrees

To find:

The between the tourist and the Statue of Liberty.

Solution:

Using the given information, draw a figure as shown below.

In a right triangle,

`\tan \theta=(Perpendicular)/(Base)`

In the triangle ABC,

`\tan 9^\circ=(305)/(x)`

`x=(305)/(\tan 9^\circ)`

`x=1925.6942`

`x\approx 1926`

Therefore, the tourist is standing 1926 feet from the Statue of Liberty.