Question

PRYZ is a rhombus. If RK = 5, RY = 13 and YRZ =67, find each measure.

Answer 1

So,

Given RK=5, RY=13 and the measure of angle YRZ=67, we're going to find the measure of KY.

Notice the following:

The diagonals of a rhombus cut and form a perpendicular segment. Thus, we obtain the following right triangle:

To find KY, we could use the pythagorean theorem:

$\begin{gathered} KY^2=13^2-5^2 \\ KY=\sqrt[]{169-25} \\ KY=\sqrt[]{144} \\ KY=12 \end{gathered}$

Therefore, KY=12.