Question

A 17-meter piece of string is stretched from the top of a 15-meter flagpole to the ground. How far is the base of the flagpole from from the end of the piece of string?

Answer 1

Distance between base of the flagpole from from the end of the piece of string is 8 meter

Solution:

Given that 17-meter piece of string is stretched from the top of a 15-meter flagpole to the ground

To find: Distance between base of the flagpole from from the end of the piece of string

The diagram is attached below

The flagpole and ground and string forms a right angled triangle

In the right angled triangle, ABC

AB = height of flag pole = 15 meter

AC = length of string = 17 meter

BC = "x" = Distance between base of the flagpole from from the end of the piece of string

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,

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

$17^2 = 15^2 + x^2\\\\289 = 225 + x^2\\\\x^2 = 64\\\\\text{Taking square root on both sides }\\\\x = \sqrt{64}\\\\x = \pm 8$

As length cannot be negative, ignore negative value

x = 8

Thus distance between base of the flagpole from from the end of the piece of string is 8 meter