Question

13) A 120 foot dock sitsalong the bank of a river. Asurveyor stands directly across theriver from one end of the dock. Fromwhere he stands the angle betweenthe lines of sight to the two ends ofthe dock is 30°. How wide is the riverto the nearest foot?

Answer 1

Given the information on the problem, we can draw the following diagram:

notice that we have a right triangle,then, we can find the value of 'w' by using the trigonometric function tangent on the angle:

`\begin{gathered} \tan (30)=\frac{\text{opposite side}}{adjacent\text{ side}}=(120)/(w) \\ \Rightarrow\tan (30)=(120)/(w) \\ \Rightarrow w\cdot\tan (30)=120 \\ \Rightarrow w=(120)/(\tan (30))=207.8\approx208ft \\ w=208ft \end{gathered}`

therefore, the river is 208 ft wide