Question

determine the measure of <r to the nearest degree. select one: a. 52° b. 54° c. 50° d. 56°

Explanation:

Step1: Apply the sine - law

The sine - law states that $\frac{\sin P}{q}=\frac{\sin R}{p}=\frac{\sin Q}{r}$. Here, $P = 80^{\circ}$, $p = 11.0$ cm and $q = 8.8$ cm. We want to find $\sin R$, so we use the formula $\frac{\sin P}{q}=\frac{\sin R}{p}$.

Step2: Rearrange for $\sin R$

$\sin R=\frac{p\sin P}{q}$. Substitute $p = 11.0$, $q = 8.8$ and $P = 80^{\circ}$ into the formula. $\sin R=\frac{11.0\times\sin80^{\circ}}{8.8}$.

Step3: Calculate $\sin R$

First, $\sin80^{\circ}\approx0.9848$. Then $\frac{11.0\times0.9848}{8.8}=\frac{10.8328}{8.8}\approx1.231$. This is incorrect. We should use $p = 8.8$ and $q = 11.0$. So $\sin R=\frac{8.8\times\sin80^{\circ}}{11.0}$. Since $\sin80^{\circ}\approx0.9848$, then $\sin R=\frac{8.8\times0.9848}{11.0}=\frac{8.66624}{11.0}\approx0.7878$.

Step4: Find the angle $R$

$R=\sin^{- 1}(0.7878)$. Using a calculator, $R\approx52^{\circ}$.

Answer:

A. $52^{\circ}$