The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:

Question

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 14 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.

(Sorry I couldn't attach the figure with the question, so I added the description)

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

A. 8.1

B. 6.2

C. 5.9

D. 7.4

Answer 1

I will let you do the exact arithmetic. Draw a figure. Angle ACB = 45 degrees.

That means the triangle you have described is an isosceles right triangle.

That means that length of AB is also 14".

Triangle DBC is a 30-60 right triangle which means DB is (14/3)sqrt(3) and

AD is 14-length of DB.

Remember that in a 30-60 right triangle the ratio of the sides is 2:1:sqrt(3).