Question

consider the following triangle. apply the law of sines to the triangle to find the missing angle (in degrees). (round your answer to one decimal place.) for triangle pqr we have $\frac{sin(\theta)}{9}=\frac{sin(50^{circ})}{8}$, so $\theta = 0.9$ i × °.

Explanation:

Step1: Apply Law of Sines formula

The Law of Sines states that $\frac{\sin\theta}{p}=\frac{\sin Q}{q}$, where $p = 8$, $q = 9$, and $Q=50^{\circ}$. So we have $\frac{\sin\theta}{8}=\frac{\sin(50^{\circ})}{9}$.

Step2: Solve for $\sin\theta$

Cross - multiply to get $\sin\theta=\frac{8\times\sin(50^{\circ})}{9}$. Since $\sin(50^{\circ})\approx0.766$, then $\sin\theta=\frac{8\times0.766}{9}=\frac{6.128}{9}\approx0.681$.

Step3: Find $\theta$

We know that $\theta=\sin^{- 1}(0.681)$. Using a calculator, $\theta=\sin^{-1}(0.681)\approx42.9^{\circ}$.

Answer:

$42.9^{\circ}$