Question

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

Explanation:

Step1: Identify trig - ratio

In right - triangle $\triangle GHF$, we know the hypotenuse $HF = 2$ and we want to find the side $GF=x$ opposite to the angle $\angle H = 26^{\circ}$. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(26^{\circ})=\frac{x}{2}$

Step2: Solve for $x$

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

Step3: Round to the nearest tenth

Rounding $0.8768$ to the nearest tenth gives $0.9$.

Answer:

$0.9$