A husband and wife are building a tiny house for a vacation getaway, and they want to measure the height of the roof of the house to see if they will be able to have a bedroom on the second floor. One side of the house is 18 ft long and the slant height of the roof along this side is 13 ft. The point on the roof\'s peak is above the center of the house. What is the height of the roof of the house? Round your answer to the nearest hundredth. Question 4 options: 9.38 ft 11.28 ft 15.21 ft 9.4
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facundo3141592 2 years ago
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By using a right triangle as a model, we will see that height of the roof is 9.38 ft.

### What is the height of the roof of the house?

The slant height is equivalent to the hypotenuse of a right triangle, so we know the length of the base and the hypotenuse of a right triangle. The cathetus will be half of 18ft

We need to find the other cathetus, so we can use the Pythagorean theorem, if X is the other cathetus we will get:

X^2 + (9ft)^2 = (13 ft)^2

X = √( (13 ft)^2 - (9 ft)^2) = 9.38ft

So the height of the roof is 9.38 ft.