Question

solve for ( x ). round to the nearest tenth, if necessary.
triangle image with right angle at l, angle at m is ( 31^circ ), side ( mk = 96 ), side ( ml = x )

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta=31^\circ$, adjacent side is $x$, hypotenuse is $96$.

Step2: Rearrange to solve for $x$

Isolate $x$ by multiplying both sides by 96.
$x = 96 \times \cos(31^\circ)$

Step3: Calculate the value

Use $\cos(31^\circ)\approx0.8572$.
$x \approx 96 \times 0.8572$

Answer:

$82.3$