An architect drew the sketch below while designing a house roof. The dimensions shown are for the interior of the triangle.
What is the value of
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Because the triangle is isosceles, constructing a perpendicular from the top vertex to the opposite side will bisect the base and create two smaller right triangles. In a right triangle, the cosine of an acute angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse. This gives which can be simplified to
Students must make use of properties of triangles to solve a problem.