Question

5 Type the correct answer in the box Round your answer to the nearest hundredth Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26° Scarlett's height is 1.65 meters, so the height of the dam is meters

Answer 1

I sletched Scarlets position (S), her distance from the dam and the angle of elevation

As you can see, they form a rigth triangle.

The side represented by the dam is the opposite side to the angle of elevation

Using the trigonometric ratios you can calculate the height of the dam

The ratio that relates the oposite and adjacent sides of an angle is the tangent

`\begin{gathered} \tan \theta=(opposite)/(adjacent) \\ \text{opposite}=\tan \theta\cdot adjacent \end{gathered}`
`\begin{gathered} \text{opposite=tan26}\cdot90 \\ \text{opposite}=43.895\cong43.90m \end{gathered}`

The dam is 43.90m