Question

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

Explanation:

Step1: Use the property of alternate - interior angles

Since the two horizontal lines are parallel, the angle inside the right - triangle (opposite to side \(y\)) is \(31^{\circ}\).

Step2: Apply the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 31^{\circ}\), the opposite side is \(y\), and the adjacent side is \(400\) ft. So, \(\tan(31^{\circ})=\frac{y}{400}\).

Step3: Solve for \(y\)

We know that \(\tan(31^{\circ})\approx0.60086\). Then \(y = 400\times\tan(31^{\circ})\). Substitute the value of \(\tan(31^{\circ})\): \(y=400\times0.60086 = 240.344\).

Answer:

\(240.3\) ft