Question

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

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

a. 6.8 inches
b. 6.2 inches
c. 3.2 inches
d. 2.8 inches

Answer 1

Find AB and DB, then subtract to get AD.

Answer 2

@fbi2015 @Isaiah.Feynman ????

Answer 3

6.8 inches. Can't explain now, I'm leaving the school to go home.

Answer 4

notice your triangle, recall your identities http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png

the angle comprising AB is 30+15 degrees, thus 45 degrees

use the tangent identity, you have the angle and the adjacent side, so you want the "opposite side", which is AB, so solve for the "opposite" in the identity

Answer 5

\(\bf tan(\theta)=\cfrac{\textit{opposite}}{\textit{adjacent}}\implies tan(\theta)\cdot \textit{adjacent}=\textit{opposite}\\ \quad \\
tan(45^o)=\cfrac{AB}{16}\implies tan(45^o)\cdot 16=AB\)

Answer 6

you'd do the same to find DB, then as maf said, substract the smaller from the longer side