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 $LM=4$, adjacent side is $LN=x$.

Step2: Rearrange to solve for $x$

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

Step3: Calculate value

First, $\tan(65^\circ)\approx2.1445$, so $x\approx\frac{4}{2.1445}\approx1.9$

Answer:

$1.9$