Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric relation

In right - triangle KLM, we know the side opposite the given angle and we want to find the hypotenuse. We use the sine function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 25^{\circ}$, the opposite side to $\theta$ is $KL = 3.1$ and the hypotenuse is $x$. So, $\sin(25^{\circ})=\frac{3.1}{x}$.

Step2: Solve for x

We can rewrite the equation as $x=\frac{3.1}{\sin(25^{\circ})}$. Since $\sin(25^{\circ})\approx0.4226$, then $x=\frac{3.1}{0.4226}$.

Step3: Calculate the value of x

$x=\frac{3.1}{0.4226}\approx7.3$.

Answer:

$7.3$