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:
[tex]\tan (\theta)=\frac{a}{b}[/tex]
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:
[tex]\begin{gathered} \tan (58)=\frac{h}{41m} \\ \Rightarrow h=\tan (58)\times41m \end{gathered}[/tex]
Use a calculator to find the value of that expression, involving the tangent of 58°:
[tex]h=65.6137\ldots m[/tex]
To the nearest integer, the height of the pyramid is:
[tex]66m[/tex]
