Question

A boat it stationed in the middle of the ocean. A treasure has been spotted 85 feet below the surface of the water at angle of depression of 30 degrees. The captain is sure that he can hook the small treasure with a line.

If the capitán wants to know the length of fishing line he will need to hook the small treasure , what special triangle relationship can be used to solve the problem ?

Answer 1

To solve this problem, we can use the special triangle relationship known as the tangent ratio. The length of the fishing line can be found using the equation x = 85/tan(30 degrees), where x is the length of the fishing line. The length of the fishing line is approximately 147.42 feet.

Step-by-step explanation:

To solve this problem, we can use the special triangle relationship known as the tangent ratio.

The tangent ratio states that the tangent of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle.

In this problem, the angle of depression is 30 degrees and the side opposite the angle is 85 feet (the depth of the treasure).

We want to find the length of the fishing line, which will be the hypotenuse of the triangle.

Using the tangent ratio, we can set up the equation: tan(30 degrees) = 85/x, where x is the length of the fishing line. Rearranging the equation, we have: x = 85/tan(30 degrees).

Substituting the value of tan(30 degrees), we can find the length of the fishing line to be approximately 147.42 feet.