Question

The Statue of Liberty the Approximately 305 feet tall. The angle of elevation of a ship to the top of the statue is 23.7 degrees how ,far to the nearest foot, is The ship on the statue base?

Answer 1

Answer:

695 feet.

Step-by-step explanation:

Please find the attachment.  

Let x represent distance between ship and base of statue.

We have been given that the Statue of Liberty is approximately 305 feet tall. The angle of elevation of a ship to the top of the statue is 23.7 degrees. We are asked to find the distance between ship and base of statue.

We can see that angle of elevation forms a right triangle with base of statue and ship.

Now, we will use tangent to solve for x as:

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(23.7^{\circ})=\frac{305}{x}$

$x=\frac{305}{\text{tan}(23.7^{\circ})}$

$x=\frac{305}{0.438969309852}$

$x=694.80939\approx 695$

Therefore, the ship is approximately 695 feet away from the base of statue.