Question

solve for x. round to the nearest tenth, if necessary. triangle lmn with right angle at m, mn = 4, angle at n is 65 degrees, and ln = x

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta=65^\circ$, opposite side to $\angle N$ is $ML$, adjacent side is $MN=4$, and $x=ML$.

Step2: Substitute values into formula

$\tan(65^\circ)=\frac{x}{4}$

Step3: Solve for $x$

Rearrange to isolate $x$: $x=4\times\tan(65^\circ)$
Calculate $\tan(65^\circ)\approx2.1445$, so $x\approx4\times2.1445$

Step4: Compute final value

$x\approx8.578$
Round to nearest tenth: $x\approx8.6$

Answer:

$8.6$