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,

$\tan \theta=\dfrac{Perpendicular}{Base}$

In the triangle ABC,

$\tan 9^\circ=\dfrac{305}{x}$

$x=\dfrac{305}{\tan 9^\circ}$

$x=1925.6942$

$x\approx 1926$

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