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. Show your work.

We have been given that 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.

We can see from our attachment that the boat, shoreline and position of person forms a right triangle, where side with 20 feet length is opposite side and x is hypotenuse for our given angle.

Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use Sine to find the value of x.

[tex]\text{Sine}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

Upon substituting our given values in above formula we will get,

[tex]\text{Sin}(60)=\frac{20}{x}[/tex]

[tex]x=\frac{20}{\text{Sin}(60)}[/tex]

[tex]x=\frac{20}{0.866025403784}[/tex]

[tex]x=23.094\approx 23.09[/tex]

Therefore, the person is 23.09 feet away from the boat.