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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?

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 Alon class=

Sagot :

SOLUTION:

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:

[tex]\begin{gathered} \\ Using\text{ Trignometry, we have that:} \\ tan\text{ 29.2}^0\text{ =}\frac{opposite\text{ }}{adjacent}=\frac{y}{116} \end{gathered}[/tex][tex]\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}[/tex]

CONCLUSION:

The width of the river is:

[tex]y=\text{ 65 m \lparen correct to the nearest metre\rparen}[/tex]

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