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 \( \triangle GHI\) with right - angle at \(H\), we know the side opposite to angle \(G\) (\(HI = 2.1\)) and we need to find the hypotenuse (\(x\)). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 64^{\circ}\), opposite side \(a = 2.1\), and hypotenuse \(c=x\). So, \(\sin(64^{\circ})=\frac{2.1}{x}\).

Step2: Solve for \(x\)

From \(\sin(64^{\circ})=\frac{2.1}{x}\), we can cross - multiply to get \(x=\frac{2.1}{\sin(64^{\circ})}\).
We know that \(\sin(64^{\circ})\approx0.8988\). Then \(x=\frac{2.1}{0.8988}\).
\(x\approx2.3\)

Answer:

\(2.3\)