The bottom of a ladder must be placed 7 feet from a wall. The ladder is 25 feet long. How far above the ground does the ladder touch the wall?
Answers
Answer:
The height is approximately
11
ft
7
in
.
Answer:
8feet
Step-by-step explanation:
You have a right triangle. The 25 ft in your hypotenuse and 7 ft is one of the sides. The other side can be found with Pythagorean's Theorem,
a^2 + b^ 2 = c^2
7^2 + b^2 = 25^2
49 + b^2 = 625
b^2 = 576
b = 24
So the top of the ladder is 24 feet up. If it goes down by 4 feet, it is now 20 feet up. The length of the ladder does not change, so our hypotenuse is still 25. So finding the other leg we get
a^2 + 20^2 = 25^2
a^2 + 400 = 625
a^2 = 225
a = 15
So the foot of the ladder is now 15 feet away from the building. Be careful, now the question is asking though, how many feet did it slide out. So we starting at 7 feet away from the building, we are now 15 feet away from the building, so we slide out 8 feet (15–7). So our answer is 8 feet.