Question

A 12-foot cable attached to the top of the mast of a sailboat is fastened to a point on the deck 4 feet from the base of the mast. What is the height of the mast?

Answer 1

The height of the mast is 8√2 feet

Explanation:

In this question, we are asked to calculate the height of the mast given the information in the question.

Please check the attachment for diagrammatic representation.

From the diagrammatic representation, we can conclude that we are asked to calculate the value of the third side of a right angled triangle, given the length of the two other sides.

Using the pythagoras’s theorem;

Square of hypotenuse = square of opposite + square of adjacent

From the diagram, we can see that the length of the cable represents the hypotenuse.

Hence;

AB^2= BC^2 + AC^2

12^2 = 4^2 + AC^2

144 = 16 + AC^2

AC^2 = 144 - 16

AC^2 = 128

AC = √128

AC = 8√2 feet