The base of a 50 foot ladder rests 33.6 feet from the side of the house. How far up the side of a house does the top of the ladder reach?

The base of a 50 foot ladder rests 33.6 feet from the side of the house. How far up the side of a house does the top of the ladder reach?

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This just a right triangle problem that we can solve with the Pytagorean Theorem..

The hypoteneuse is 50 and one of the legs is 33.6. So, to find the other leg, we have...

SQRT (50² - 33.6²) ≈ 37.03 ft up the side of the house

This is a right triangle with hypotenuse equal to the length of the ladder, 50 feet, and one leg equal to 33.6 feet.

By the Pythagorean theorem we have

$$50^2=(33.6)^2+h^2$$

$${{\mathtt{50}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\left({\mathtt{33.6}}\right)}^{{\mathtt{2}}} = {\mathtt{1\,371.04}}$$

$${\mathtt{h}} = {\sqrt{{\mathtt{1\,371.04}}}} = {\mathtt{h}} = {\mathtt{37.027\: \!557\: \!305\: \!336\: \!791\: \!6}}$$

so about 37.03 feet up the side of the house.