Question

find the value of x. round all answers to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 65^{\circ}\), the opposite side to the \(65^{\circ}\) angle is \(10\), and the hypotenuse is \(x\). So, \(\sin65^{\circ}=\frac{10}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(x=\frac{10}{\sin65^{\circ}}\). We know that \(\sin65^{\circ}\approx0.9063\). Then \(x=\frac{10}{0.9063}\approx11.03\).

Answer:

\(11.03\)