Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine function is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, for angle $x$, the opposite side is $MN = 1.1$ and the hypotenuse is $NL=2.6$.

Step2: Set up the equation

We have $\sin x=\frac{1.1}{2.6}$.

Step3: Solve for $x$

Using the inverse - sine function $x = \sin^{-1}(\frac{1.1}{2.6})$.
Calculate $\frac{1.1}{2.6}\approx0.423$.
Then $x=\sin^{-1}(0.423)$.
Using a calculator, $x\approx25.0^{\circ}$.

Answer:

$25.0^{\circ}$