Question

A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 116 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is = 29.2°. How wide is the river?

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The width of the river can see calculated thus:

`\begin{gathered} \\ Using\text{ Trignometry, we have that:} \\ tan\text{ 29.2}^0\text{ =}\frac{opposite\text{ }}{adjacent}=(y)/(116) \end{gathered}`
`\begin{gathered} cross-multiply,\text{ we have that:} \\ y\text{ = 116 x tan 29.2}^0 \\ Then,\text{ } \\ y\text{ = 116 x 0.5589} \\ y\text{ = 64.8324 m} \\ y\text{ }\approx\text{ 65 m \lparen to the nearest metre\rparen} \end{gathered}`

CONCLUSION:

The width of the river is:

`y=\text{ 65 m \lparen correct to the nearest metre\rparen}`