Question

- A boat is 12 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 34° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the

nearest tenth of a foot. Show all work.

Answer 1

distance = 7.4 ft

Explanation:

There are different ways to approach this problem, but one possible method is to use trigonometry. Since we know the angle and one side of the triangle formed by the boat, the person, and the closest point to the boat, we can use the sine, cosine, or tangent function to find the other sides. For example, we can use the tangent function:

tan(34°) = opposite / adjacent

opposite = adjacent * tan(34°)

We know that the opposite side is the distance from the person to the boat, and the adjacent side is the distance from the person to the closest point to the boat, which is 12 ft. Therefore, we can substitute these values into the equation:

distance = 12 ft * tan(34°)

To find the distance, we need to know the value of the tangent of 34°. We can use a calculator or a trigonometry table to get this value, which is approximately 0.6167. Then we can substitute this value into the equation and solve for distance:

distance = 12 ft * 0.6167

distance = 7.4004 ft

Rounding to the nearest tenth of a foot, the person is about 7.4 ft away from the boat.

Another way to solve this problem is by using the law of sines.

distance = (12*sin(34))/(sin(126))

distance = 7.4 ft