Question

1. find the value of x.

type a response

Explanation:

Step1: Identify the trigonometric function

In a right - triangle, for an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 40^{\circ}\), the opposite side to the \(40^{\circ}\) angle is \(x\), and the hypotenuse is \(15\).
So, \(\sin40^{\circ}=\frac{x}{15}\).

Step2: Solve for \(x\)

We know that \(\sin40^{\circ}\approx0.6428\).
From \(x = 15\times\sin40^{\circ}\), substituting the value of \(\sin40^{\circ}\), we get \(x=15\times0.6428\).
\(x = 9.642\approx9.6\)

Answer:

\(x\approx9.6\)