Question

find the value of x, correct to 1 decimal place.

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 26^{\circ}$, the opposite side to the angle $\theta$ is $12$ m and the hypotenuse is $x$. So, $\sin26^{\circ}=\frac{12}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{12}{\sin26^{\circ}}$. Since $\sin26^{\circ}\approx0.4384$, then $x=\frac{12}{0.4384}\approx27.4$.

Answer:

$27.4$