Question

solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 2
x =
submit answer

Explanation:

Step1: Identify adjacent side, hypotenuse

We have right triangle $\triangle MNL$, right-angled at $M$. For $\angle N = 65^\circ$, adjacent side $MN = 4$, hypotenuse $NL = x$.

Step2: Use cosine ratio formula

Cosine of an angle in right triangle is $\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(65^\circ) = \frac{4}{x}$

Step3: Rearrange to solve for $x$

$x = \frac{4}{\cos(65^\circ)}$
Calculate $\cos(65^\circ) \approx 0.4226$, so $x \approx \frac{4}{0.4226} \approx 9.5$

Answer:

$9.5$