Question

find the length of side x to the nearest tenth.
answer attempt 1 out of 2
x =

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the hypotenuse is \(\sqrt{11}\), and the side opposite to \(30^{\circ}\) is \(x\).
So, \(\sin30^{\circ}=\frac{x}{\sqrt{11}}\).
Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{x}{\sqrt{11}}\).

Step2: Solve for \(x\)

Cross - multiply: \(x=\frac{\sqrt{11}}{2}\).
Calculate \(\sqrt{11}\approx3.3166\). Then \(x=\frac{3.3166}{2}=1.6583\approx1.7\).

Answer:

\(1.7\)