Question

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

Explanation:

Step1: Identify trigonometric relation

In right - triangle DEF, we know the hypotenuse DF = 52 and the angle ∠D=18°. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin D=\frac{EF}{DF}$, and we want to find EF which is $x$. So, $\sin(18^{\circ})=\frac{x}{52}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin(18^{\circ})=\frac{x}{52}$ by 52. We get $x = 52\times\sin(18^{\circ})$.
We know that $\sin(18^{\circ})\approx0.309$. Then $x = 52\times0.309 = 16.068$.

Step3: Round the answer

Rounding $16.068$ to the nearest tenth, we get $x\approx16.1$.

Answer:

$16.1$