Question

A 12 - ft ladder leans against the side of a house. the bottom of the ladder is 9 ft from the side of the house. how high is the top of the ladder from the ground? if necessary, round your answer to the nearest tenth.

Answer 1

Here, you can apply the Pythagorean theorem:  to the right triangle formed by the ladder as the hypotenuse (side c), the wall of the building as the vertical side (side a) and the distance of the bottom of the ladder from the base of the building as the base of the right triangle, (side b).
So you are looking for the length of side a (the height the ladder reaches on the building) of the right triangle when you know the lengths of the other two sides.
 Substitute c = 16 ft. (The ladder) and b = 5 ft. (The distance of the bottom of the ladder from the base of the wall)

 Simplify and solve for a.
 Subtract 25 from both sides.
 Take the square root of both sides.
 Round to the nearest tenth.
 feet. 15.2 is the answer.

Answer 2

Answer: 7.9 ft.

Step-by-step explanation:

Given : The length of ladder = 12 ft.

The distance of bottom of the ladder from the side of the house = 9^29 ft.

Since the side of the house must be standing vertical to the ground makinf right angle, then the triangle made by ladder must be a right angle with hypotenuse (Side opposite to right angle) = 12 ft.

Let x be the height of the top of the ladder from the ground.

Using the Pythagoras theorem of right triangles, we have

$12^2=9^2+x^2\\\\\Rightarrow\ x^2=144-81\\\\\Rightarrow\ x^2=63\\\\\Rightarrow\ x=\sqrt{63}=7.9372539331\approx7.9$

Hence, the height of the top of the ladder from the ground = 7.9 ft.