Question

solve for x. round to the nearest tenth, if necessary. triangle mlk with right angle at l, angle at m is 64 degrees, length of lk is 8.5, length of mk is x

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
Here, $\theta=64^\circ$, opposite side $=8.5$, hypotenuse $=x$.

Step2: Substitute values into ratio

$\sin(64^\circ)=\frac{8.5}{x}$

Step3: Rearrange to solve for $x$

$x=\frac{8.5}{\sin(64^\circ)}$

Step4: Calculate value

First, $\sin(64^\circ)\approx0.8988$, so $x\approx\frac{8.5}{0.8988}\approx9.5$

Answer:

$9.5$