Question

if a tree 20 meters tall casts a shadow 30 meters long, what is the angle of elevation from the shadow to the tip of the tree, to the nearest degree?

Answer 1

sketch the situation

a trigonometric function that is a relation between the angle of elevation and the 2 sides of the rectangles is the tan

$\tan \theta=\frac{opp}{adj}$$\tan \theta=\frac{20}{30}=\frac{2}{3}$

find the inverse

$\begin{gathered} \tan ^{-1}(\frac{2}{3})=\theta \\ \theta=33.69º \end{gathered}$

after rounding the angle of elevation is 34º.