The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced: Triangle ABC has length of BC equal to 12 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees, and measure of angle DCB is 30 degrees.

What is the length of the wood that is needed to replace AD?

6.2 inches
4.2 inches
6.9 inches
5.1 inches

The answer is 5.1 inches

Step-by-step explanation:

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.

Whole triangle:

Tan 45 = x/12

x = 12 * tan 14

x = 12 * 1

x = 12

Just the 30 degree triangle:

Tan 30 = x/12

x = 12 * tan 30

x = 12 * 0.577

x = 6.924

Now you subtract the smaller 30 degree triangle from the whole triangle to find the measure of AD.

12 - 6.924 = 5.076 which rounds to 5.1

I also took the test with this same question and got it correct.

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step-by-step explanation: