Question

solve for y. do not convert your answer to decimal form. rationalize the denominator and simplify your answer if necessary. draw y 10 60° show your work here hint: to add the square root symbol (√), type root

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 60^{\circ}\), the opposite side to the \(60^{\circ}\) angle is \(y\), and the hypotenuse is \(10\). So, \(\sin60^{\circ}=\frac{y}{10}\).

Step2: Substitute the value of \(\sin60^{\circ}\)

We know that \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\). Then \(\frac{\sqrt{3}}{2}=\frac{y}{10}\).

Step3: Solve for \(y\)

Cross - multiply: \(y = 10\times\frac{\sqrt{3}}{2}\). Simplify the right - hand side: \(y = 5\sqrt{3}\).

Answer:

\(y = 5\sqrt{3}\)