MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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[tex]12^2=9^2+x^2\\\\\Rightarrow\ x^2=144-81\\\\\Rightarrow\ x^2=63\\\\\Rightarrow\ x=\sqrt{63}=7.9372539331\approx7.9[/tex]Hence, the height of the top of the ladder from the ground = 7.9 ft.