Question

Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and Suzie to be 30°. Suzie approximates the angle formed by the lead boat, herself, and Swanson to be 130°. How far is the boat from Swanson?

Show your work. Write out the equation you will use. Round your answer to the nearest tenth.

Answer 1

The distance from the boat to Swanson can be calculated using the Law of Sines, given the angles from Swanson and Suzie's perspectives and the distance separating them. By solving the equation with the known angles and the distance between them, we find that the boat is approximately 56.1 feet away from Swanson.

Step-by-step explanation:

The question involves solving a geometry problem using the Law of Sines. We have two people, Swanson and Suzie, who are standing 35 feet apart and observing a boat. We know two angles from their respective positions: Swanson's angle is 30° and Suzie's angle is 130°. To find the distance from the boat to Swanson (d), we can use the fact that the sum of the angles in any triangle is 180° to determine the angle at the boat's position. That angle will be 180° - 30° - 130° = 20°. Now we have a triangle with all three angles known and one side known (the distance between Swanson and Suzie).

Using the Law of Sines:

sin(30°) / d = sin(20°) / 35

We can cross-multiply to find the distance d:

d = 35 * sin(30°) / sin(20°)

After calculating, we round the answer to the nearest tenth:

d ≈ 56.1 feet (rounded to one decimal place)