Question

In AXYZ, ZX=13° and XY=63º. ZXWZ=90° and XY=690. Find the length of XW to
the nearest 10th.

Answer 1

We want to find WZ, so we focus on right triangle YWZ. Side WY is half the length of XY because WZ is a line bisector of XY. Therefore, YW is 4.25

Now, we have a right triangle with a known angle and a known side. With this type of triangle, we can use basic trigonometry applications.

The side opposite to the 90 degree angle is the hypotenuse. The hypotenuse is YZ. The two legs are WZ and YW.

We can use cosine function to find tangent because the YZ is not known.

tangent is side opposite of angle divided by side adjacent to angle.

tan(72) = WZ / 4.25

4.25tan(72) = WZ

0.3 = WZ