M:C:SPR:4

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Additional Topics in Math

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An architect drew the sketch below while designing a house roof. The dimensions shown are for the interior of the triangle.

The figure presents a triangle with 2 labeled sides and 2 labeled angles. The base of the triangle is labeled 32 feet, and the side to the left of the base is labeled 24 feet. The two interior angles to the left and to the right of the base are labeled x degrees. A note under the figure says that the figure is not drawn to scale.

What is the value of $cos space x ?$

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$bold 2 over bold 3$

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 $cos space x equals 16 over 24 comma$ which can be simplified to $cos space x equals 2 over 3.$

Question Difficulty:

hard

Objective:

Students must make use of properties of triangles to solve a problem.

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Question 30 of 30

M:C:SPR:4

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