Question

question 1 1 points save answer a surveyor wants to find the distance d across a river. a stake is placed on each bank of the river as shown in the figure. she measures a distance of 30.0 m from one stake to another on the same side of the river, thus finding the third vertex on a right triangle. she then measures the angle θ and finds it equal to 75.9°. what is the distance d across the river? 29.0 m 268 m 89.2 m 15.3 m 119 m

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side is \(d\) (the distance across the river) and the adjacent side is \(30.0\ m\), and \(\theta = 75.9^{\circ}\). So, \(\tan(75.9^{\circ})=\frac{d}{30.0}\).

Step2: Solve for \(d\)

We know that \(d = 30.0\times\tan(75.9^{\circ})\). Using a calculator, \(\tan(75.9^{\circ})\approx3.97\). Then \(d=30.0\times3.97 = 119.1\approx119\ m\).

Answer:

\(119\ m\)