Question

solve for x. round to the nearest tenth, 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, $\theta = 26^{\circ}$, the opposite side to the angle $\theta$ is $x$ and the hypotenuse is $2$.

Step2: Apply the sine formula

We have $\sin(26^{\circ})=\frac{x}{2}$.

Step3: Solve for $x$

Multiply both sides of the equation by $2$: $x = 2\times\sin(26^{\circ})$.
Using a calculator, $\sin(26^{\circ})\approx0.4384$. Then $x = 2\times0.4384=0.8768$.

Answer:

$0.9$