Question

a ladder touches a wall 15ft off the ground, and the base of the ladder is 8 feet from the base of the wall. how long is the ladder

Answer 1

The length of ladder is 17 feet

Solution:

Given that, ladder touches a wall 15 ft off the ground, and the base of the ladder is 8 feet from the base of the wall

To find: length of ladder

The ladder, wall and ground forms a right angled triangle

Where, ladder is "hypotenuse" and "ground' forms the base

The figure is attached below

ABC is a right angled triangle

AC = length of ladder = ?

AB = height of wall = 15 feet

BC = distance between base of ladder and base of wall = 8 feet

Apply pythogoras theorem for right angled triangle

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 theorem,

`AC^2 = AB^2+BC^2`

Substituting the values we get,

`AC^2 = 15^2 + 8^2\\\\AC^2 = 225 + 64\\\\AC^2 = 289\\\\\text{Take square root on both sides }\\\\AC = √(289)\\\\AC = 17`

Thus length of ladder is 17 feet