Question

solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(DEF\) with \(\angle D = 18^{\circ}\), hypotenuse \(DF = 52\), and opposite side to \(\angle D\) is \(x\). Use the sine ratio \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin(18^{\circ})=\frac{x}{52}\).

Step2: Solve for \(x\)

Multiply both sides of the equation by \(52\): \(x = 52\times\sin(18^{\circ})\).
We know that \(\sin(18^{\circ})\approx0.3090\).
Then \(x = 52\times0.3090=16.068\).

Answer:

\(x\approx16.1\)