Question

A scuba diver has a rope connecting the dive boat to an anchor on the ocean floor. The rope is 13ft long. The water is 5ft deep. How far is the anchor from a point directly below the boat?

Answer 1

The anchor is 12 feet far from the point directly below the boat.

Explanation:

Given that:

Length of rope connecting the dive boat to an anchor = 13 feet

Depth of water = 5 feet

Here,

The rope connecting the dive boat to the anchor will serve as hypotenuse of a right angle triangle, depth of water will be the height of triangle and distance from anchor to point directly below the boat will be base of triangle.

Using Pythagorean theorem;

`a^2+b^2=c^2`

a = 5 , c = 13

`(5)^2+b^2=(13)^2\\25+b^2=169\\b^2=169-25\\b^2=144`

Taking square root on both sides

`√(b^2) =√(144)\\b=12`

Hence,

The anchor is 12 feet far from the point directly below the boat.