Question

A 25-ft rope is stretched from the top of

Answer 1

The height of mast is 19.21 feet

Solution:

Given that, 25-ft rope is stretched from the top of  a ship's mast to a cleat on the deck

The cleat is 16 ft from the base of the  mast

To find: height of mast

The ship mast, deck and base forms a right angled triangle

The figure is attached below

AC = length of rope = 25 feet

BC = distance between base of mast and cleat = 16 feet

AB = height of mast = ?

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle

By above definition for right angled triangle ABC,

$AC^2=AB^2+BC^2$

$25^2=AB^2+16^2$

$625 = AB^2+256\\\\AB^2=625-256\\\\AB^2=369\\\\\text{Take square root on both sides }\\\\AB = \sqrt{369}\\\\AB = 19.21$

Thus height of mast is 19.21 feet