Answer:
The height of the house is between 9 and 10 feet.
Step-by-step explanation:
The shaped formed with the ground, the ladder, and the house is a right triangle.
I'm going to apply Pythagorean Theorem here.
The length of the hypotenuse is given as 24 feet.
The length from the base of the ladder and the house is 22 feet.
So to find the height the ladder reaches on the house, we need to solve
[tex]a^2+22^2=24^2[/tex]
[tex]a^2+484=576[/tex]
Subtract 484 on both sides:
[tex]a^2=576-484[/tex]
Simplify:
[tex]a^2=92[/tex]
Square root both sides:
[tex]a=\sqrt{92}[/tex]
[tex]a \approx 9.59166[/tex] feet
