Question

Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 12 yards tall casts a shadow 15 yards long. Round to the nearest degree.

Answer 1

Let us try to represent the question as an image.

From the diagram, we can get a triangle by considering the tree and shadow, such that

The angle x° is the angle of elevation of the sun,

To find the angle x°, we will use one of the Trigonometric Ratios, in this case, the Tan ratio.

Hence,

`\tan x=(opp)/(adj)`

where

opp = 12 yards

adj = 15 yards

Substituting,

`\begin{gathered} \tan x=(12)/(15) \\ \tan x=0.8 \\ x=\tan ^(-1)0.8 \\ x=38.66^(\circ) \end{gathered}`

The angle of elevation of the sun, to the nearest degree, is 39°