Question

a 12-ft ladder leans against the side of a house. the bottom of the ladder is 8 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.

Explanation:

Step1: Apply Pythagorean theorem

Let $h$ = height, ladder = hypotenuse.
$$h^2 + 8^2 = 12^2$$

Step2: Calculate squared terms

$$h^2 + 64 = 144$$

Step3: Isolate $h^2$

$$h^2 = 144 - 64 = 80$$

Step4: Solve for $h$, round to tenth

$$h = \sqrt{80} \approx 8.9$$

Answer:

8.9 ft