Question

given the triangle, find the measure of angle $x$ using the law of sines. round your final answer to 2 decimal places. the triangle is not drawn to scale. $x = \text{degrees}$

Explanation:

Step1: Apply Law of Sines formula

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Let the side opposite the $98^{\circ}$ angle be $a = 14$, the side opposite angle $x$ be $b = 10$. So, $\frac{14}{\sin98^{\circ}}=\frac{10}{\sin x}$.

Step2: Solve for $\sin x$

Cross - multiply to get $14\sin x=10\sin98^{\circ}$. Then $\sin x=\frac{10\sin98^{\circ}}{14}$.

Step3: Calculate $\sin x$ value

We know that $\sin98^{\circ}\approx0.9903$. So, $\sin x=\frac{10\times0.9903}{14}=\frac{9.903}{14}\approx0.7074$.

Step4: Find the value of $x$

$x = \sin^{- 1}(0.7074)$. Using a calculator, $x\approx44.99^{\circ}$.

Answer:

$44.99$