Question

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

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 60^{\circ}\), the opposite side is \(1\), and the hypotenuse is \(x\). So \(\sin60^{\circ}=\frac{1}{x}\).

Step2: Solve for \(x\)

Since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\), we have \(\frac{\sqrt{3}}{2}=\frac{1}{x}\). Cross - multiply gives \(x=\frac{2}{\sqrt{3}}\). Rationalize the denominator: \(x=\frac{2\sqrt{3}}{3}\approx1.2\)

Answer:

\(1.2\)