Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 26^{\circ}\), the opposite side to \(\angle H\) is \(GF=x\), and the hypotenuse \(HF = 2\).
So, \(\sin(26^{\circ})=\frac{x}{2}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(26^{\circ})=\frac{x}{2}\) by \(2\).
\(x = 2\times\sin(26^{\circ})\).
We know that \(\sin(26^{\circ})\approx0.4384\).
Then \(x=2\times0.4384 = 0.8768\approx0.9\).

Answer:

\(x\approx0.9\)