Question

find y.
round to the nearest tenth:
y = ?ft

Explanation:

Step1: Identify the trigonometric function

We know the hypotenuse (\(500\) ft) and we need to find the side \(y\) which is opposite to the angle \(29^{\circ}\). The sine function is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(29^{\circ})=\frac{y}{500}\).

Step2: Solve for \(y\)

Multiply both sides of the equation \(\sin(29^{\circ})=\frac{y}{500}\) by \(500\) to isolate \(y\). We get \(y = 500\times\sin(29^{\circ})\). Using a calculator, \(\sin(29^{\circ})\approx0.4848\). Then \(y=500\times0.4848 = 242.4\)

Answer:

\(242.4\)