Question

A person whose eye level is 1.5 meters above ground level looks at the top of a tree at an angle of `24^circ` above the horizontal. If the tree is 20 meters away, how tall is the tree?

Answer 1

Height of tree (to nearest half meter): `color(green)(10.5 " meters")`

Explanation:

Assuming the situation is as indicated in the image below:

The height of the tree is `t+1.5 m`

`t/(20 " m") = tan(24^@)`

Therefore
`color(white)("XXX")"Height of tree" = 20*tan(24^@)" m" + 1.5" m"`

(with the aid of a calculator)
`color(white)("XXXXXXXXXXXX")~~8.905+1.5" m"`

`color(white)("XXXXXXXXXXXX")~~10.4 " m"`