Question

On a boat tour in New York Harbor, Samuel views the Statue of Liberty. He knows from a brochure that the statue is 93 meters tall. If the angle formed by the water and the line segment from boat to the top of the statue form a 26.3° angle, how far is the boat from the base of the statue?

Answer 1

From the given provided, we can form a right triangle as shown in the attached diagram. Since we have the statue's height and the angle formed between the top of the boat and the statue we can use the properties of the tangent function below.

$\tan \theta = \frac{opposite}{adjacent}$
$\tan(26.3) =\frac{93}{A}$
$A = \frac{93}{\tan(26.3)}$
$A = 188$

From this, we can see that the side adjacent to the angle has a measurement of 188 m. This is actually the distance between boat and the base of the statue. 

Answer: 188 m