Question

The angle of elevation of a boy to the top of a tree is 30°. If the height of the tree is 25 feet, find the distance between the boy and the tree.

Answer 1

43.3 ft

Step-by-step explanation:

The diagram representing this problem is drawn and attached below:

The distance between the boy and the tree = x

Recall from trigonometrical ratios:

`\tan \theta=\frac{\text{Opposite}}{\text{Adjacent}}`

Therefore:

`\begin{gathered} \tan 30\degree=\frac{\text{2}5}{\text{x}} \\ \text{Cross multiply} \\ x\tan 30\degree=25 \\ x=(25)/(\tan 30\degree) \\ x=43.3\; ft \end{gathered}`

The distance between the boy and the tree is 43.3 ft (correct to 2 decimal places).