Question

find the measure of x.
11
x
28°
x = ?
round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 28^{\circ}\), the hypotenuse \(c = 11\), and the opposite side to the angle \(28^{\circ}\) is \(x\).
So, \(\sin(28^{\circ})=\frac{x}{11}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(28^{\circ})=\frac{x}{11}\) by \(11\):
\(x = 11\times\sin(28^{\circ})\).
We know that \(\sin(28^{\circ})\approx0.4695\).
Then \(x=11\times0.4695 = 5.1645\approx5.16\).

Answer:

\(5.16\)