Question

The Statue of Liberty situated at Liberty Island, New York is 93 m tall.A bird sitting on the top of the statue is viewed at 30° angle of elevationby the lens of a camera standing on the ground some distance away at aheight of 1 meter above the ground.What is the horizontal distance from the base of the statue to thecamera? Round your answer to the nearest tenth of a meter.2Required: enter an answer!mOH OK Answer

Answer 1

Given:

The height of the Statue of Liberty, h=93 m.

The angle of elevation of the bird on top of the statue as viewed by a camera on the ground, θ=30°.

The height of the camera lens with respect to the ground, y=1 m.

Let x be the horizontal distance from base of the statue to the camera.

Using trigonometric property in the above triangle,

`\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{adjacent\text{ side}} \\ \tan \theta=(h-y)/(x) \end{gathered}`

Substitute the values and solve the equation for x.

`\begin{gathered} \tan 30^(\circ)=(93m-1m)/(x) \\ x=\frac{92\text{ m}}{\tan 30^(\circ)} \\ =159.3\text{ m} \end{gathered}`

Therefore, the horizontal distance from base of the statue to the camera is m.