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,
[tex]AC^2=AB^2+BC^2[/tex]
[tex]25^2=AB^2+16^2[/tex]
[tex]625 = AB^2+256\\\\AB^2=625-256\\\\AB^2=369\\\\\text{Take square root on both sides }\\\\AB = \sqrt{369}\\\\AB = 19.21[/tex]
Thus height of mast is 19.21 feet
