Question

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

Answer 1

The Solution:

The correct answer is 67 degrees.

Given the rhombus below:

We are required to find the measure of angle PRZ.

Considering trianglePRZ, we can apply the law of cosine to the angle of interest, which is, angle PRZ.

`R=\cos ^(-1)((p^2+z^2-r^2)/(2pz))`

In this case,

`\begin{gathered} p=(5+5)=10 \\ z=13 \\ r=13 \\ R=\text{?} \end{gathered}`

Substituting these values in the formula, we get

`R=\cos ^(-1)((10^2+13^2-13^2)/(2(10)(13)))`
`R=\cos ^(-1)(\frac{100^{}+169^{}-169^{}}{2(10)(13)})=\cos ^(-1)(\frac{100^{}}{260})=67.380\approx67^o`
`m\angle\text{PRZ}\approx67^o`

Therefore, the correct answer is 67 degrees.