Question

Larry is reroofing his house. Each side of the roof measures 14 feet from the eave to the ridge. The horizontal distance between the eaves is

20 feet.
x
14 feet
14 feet
20 feet
The measure of the angle between the two sides of the roof is approximately
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Answer 1

91.2°

Explanation:

There are several ways to find the a.pex angle of an isosceles triangle with all side lengths given. One of them is using the Law of Cosines:

c² = a² +b² -2ab·cos(C)

Solving for the angle C, we find ...

C = arccos((a² +b² -c²)/(2ab))

__

Here, we have a=b=14 and c=20. The angle is ...

C = arccos((14² +14² -20²)/(2·14·14)) = arccos(-8/392)

C ≈ 91.16938°

The interior angle at the peak of the roof is about 91.2°.