Question

use the diagram below to find the distance across the river. round your answer to one decimal place.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with angle \(28^\circ\), adjacent side \(45\) ft, and opposite side \(x\) (distance across river). Use tangent: \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(28^\circ)=\frac{x}{45}\)

Step2: Solve for \(x\)

Multiply both sides by \(45\): \(x = 45\times\tan(28^\circ)\)
Calculate \(\tan(28^\circ)\approx0.5317\), so \(x\approx45\times0.5317\)
\(x\approx23.9265\), round to one decimal: \(x\approx23.9\)

Answer:

The distance across the river is approximately \(23.9\) feet.