Question

How far is the girl from the monument that is 30 ft high? Round your answer to a nearest foot. Show your work.

Answer 1

Given:

The diagram is shown alongside.

The height of the monument is 30 ft high.

The angle of elevation is 63 degrees

The objective is to find the distance between the monument and where the girl is standing.

Since it forms a right angled triangle so we can apply trigonometric ratios:

Now,

`\tan 63^(\circ)=\frac{perpendicular}{\text{base}}`

Perpendicular = 30 ft

Base = ?

Substituting the values,

`\begin{gathered} \tan 63^(\circ)=\frac{30}{\text{base}} \\ \text{Base}=(30)/(\tan63^(\circ)) \\ \text{base}=(30)/(1.962610) \\ \text{base}=15.285767422\text{ ft} \end{gathered}`

Therefore, the girl is at a distance of 15 ft from the monument.