Question

A boat is 20 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 60° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Draw a picture showing the right triangle. Round your answer to the nearest tenth of a foot.

Answer 1

Answer:

Distance of the person from the boat is 23.1 feet.

Step-by-step explanation:

We have,

The distance of the boat from the shoreline = 20 feet.

Angle between the boat and the person = 60°

So, we get the right triangle as shown in the figure.

As, in a right triangle, the angles and sides can be written in trigonometric form.

Thus, $\sin A=\frac{Perpendicular}{Hypotenuse}$

i.e. $\sin 60=\frac{20}{x}$

i.e. $0.866=\frac{20}{x}$

i.e. $x=\frac{20}{0.866}$

i.e. x = 23.1 feet.

Thus, the distance of the person from the boat is 23.1 feet.