Question

Find the width (in m) of the river in the illustration. (Round your answer to three significant digits.)

44°
100 m

Answer 1

`w \approx 96.6 \, \textrm{m}`

Explanation:

See the attached image for my labeled diagram.

To solve for
`w`, we can use the trigonometric ratio tangent.

`\tan(\theta)=\frac{\textrm{opposite}}{\textrm{adjacent}}`

`\tan(44\textdegree)=\frac{w}{100 \, \textrm{m}}`

↓ multiply both sides by 100m

`100 \, \textrm{m} \cdot \tan(44\textdegree)=w`

↓ plug
`100\, \textrm{m} \cdot \tan(44\textdegree)` into a calculator

`96.56887 \, \textrm{m} \approx w`

`w \approx 96.56887 \, \textrm{m}`

↓ round to 3 significant figures

`w \approx 96.6 \, \textrm{m}`