Question

A 14​-foot ladder is placed against a vertical wall of a​ building, with the bottom of the ladder standing on level ground 9 feet from the base of the building. How high up the wall does the ladder​ reach?

Answer 1

Answer:

10.7 feet

Step-by-step explanation:

The ladder, the ground and the wall form the shape of a right angled triangle as shown in the image below.

The hypotenuse of the triangle is 14 feet (length of ladder)

The base of the triangle is 9 feet long (the distance from the base of the ladder to the wall)

We need to find the height of the triangle. We can apply Pythagoras rule:

$hyp^2 = a^2 + b^2$

where hyp = hypotenuse

a = base of the triangle

b = height of the triangle

Therefore:

$14^2 = 9^2 + b^2\\\\196 = 81 + b^2\\\\b^2 = 196 - 81 = 115\\\\b = \sqrt{115} \\\\b = 10.7 feet$

The wall reaches 10.7 feet high.