Question

use the information in the illustration to find the height of the pyramid. round your answer to the nearest meter.

Answer 1

Notice that the height of the pyramid forms a right triangle with the shown side on the base. Remember also the definition of the tangent trigonometric function:

`\tan (\theta)=(a)/(b)`

From the figure, the side opposite to the angle of 58° is the height of the pyramid, and the side adjacent to that angle has a length of 41 meters. Then:

`\begin{gathered} \tan (58)=(h)/(41m) \\ \Rightarrow h=\tan (58)*41m \end{gathered}`

Use a calculator to find the value of that expression, involving the tangent of 58°:

`h=65.6137\ldots m`

To the nearest integer, the height of the pyramid is:

`66m`