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 a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 42^{\circ}\), the opposite side to \(\theta\) is \(x\), and the hypotenuse is \(5\).
So, \(\sin42^{\circ}=\frac{x}{5}\)

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin42^{\circ}=\frac{x}{5}\) by \(5\).
We know that \(\sin42^{\circ}\approx0.6691\)
\(x = 5\times\sin42^{\circ}\)
\(x=5\times0.6691 = 3.3455\approx3.3\)

Answer:

\(x = 3.3\)