13.10.2021

The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:
15,
Bu
10 in.
What is the length of the wood that is needed to replace AD?
0 4.2 inches
O 5.7 inches
0 2.5 inches
0 1.3 inches

. 21

Step-by-step answer

06.09.2022, solved by verified expert
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For the triangle, you would use the tangent ratio to find 45 degrees (30 + 15) and then 30 for the measure of the opposite sides.

So, for triangle ABC, 

tan (m<ABC) = Perpendicular/Base

So, tan 45 = AB/BC

tan 45 = AB/10

AB = 10 × 1 = 10

Now, for triangle DBC, 

tan (m<BDC) = BD/BC

tan 30 = BD/10

BD = 10 * 0.577

BD = 5.77

This, AD = AB - BD = 10 - 5.77 = 4.23 ≈ 4.2 inches

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