Question

solve for x. round to the nearest tenth of a degree, if necessary.

Explanation:

Step1: Identify trigonometric ratio

Since we know the adjacent side ($NO = 6.1$) and the hypotenuse ($NP=6.9$) of the right - triangle, we use the cosine function. $\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(x)=\frac{6.1}{6.9}$.

Step2: Solve for x

We take the inverse - cosine of both sides. $x = \cos^{-1}(\frac{6.1}{6.9})$.
Using a calculator, $\frac{6.1}{6.9}\approx0.8841$. Then $x=\cos^{-1}(0.8841)$.
$x\approx27.8^{\circ}$ (rounded to the nearest tenth of a degree).

Answer:

$27.8^{\circ}$