solve for x. round to the nearest tenth, if necessary.
solve for x. round to the nearest tenth, if necessary.
Answer
Explanation:
Step1: Identify trig - ratio
Since we have a right - triangle, and we know an angle and the side opposite the angle and we want to find the hypotenuse, we use the sine function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 26^{\circ}$, the opposite side to the angle $\theta$ is $GH = 6.5$ and the hypotenuse is $x$. So, $\sin(26^{\circ})=\frac{6.5}{x}$.
Step2: Solve for $x$
Cross - multiply to get $x\sin(26^{\circ})=6.5$. Then $x=\frac{6.5}{\sin(26^{\circ})}$. We know that $\sin(26^{\circ})\approx0.4384$. So, $x=\frac{6.5}{0.4384}\approx14.8$.
Answer:
$14.8$