Question

The measurement from the base of a tree to the tip of its shadow is 100 ft. The angle of inclination is 60°.Given:sin 60° = 0.866cos 60º = 0.5tan 60° = 1.732600*not drawn to scale100 ft

Answer 1

STEP 1

Interpret the question to make geometric sense of it.

We have a triangle as depicted in the diagram below.

STEP 2

Find the unknown:

h is the opposite in a right angled triangle

100ft is the adjacent

h can be gotten with the formulae below.

`\tan \emptyset=\frac{opp}{\text{adj}}`

This gives opposite to be

`\begin{gathered} \text{Adj}*\tan \emptyset\text{ where} \\ \emptyset=60\text{ deg} \end{gathered}`
`\text{Opposite = 100}*1.732=173.2\text{ ft}`

Therefore, tree height = 173.2 ft