Question

Marcos is flying a kite 35 feet above an oak tree . The angle of elevation is 16° and the angle of elevation to the kite is 25° . what is the distance , B , to the nearest foot, Marcos is standing from the tree?

Answer 1

Consider the height of oak tree be x.

Determine the relation between oak tree height and distance B by using trigonometric ratio.

`\begin{gathered} \tan 16^(\circ)=(x)/(b) \\ x=b\tan 16^(\circ) \end{gathered}`

Determine the relation between height of kite and distance B using the trigonometric ratios.

`\begin{gathered} \tan 25^(\circ)=(a)/(b) \\ a=b\tan 25^(\circ) \end{gathered}`

The difference between height of kite (a) and height of oak tree (x) is 35 ft or,

`a-x=35`

Substitute vaue a and x from the obtained to obtain the equation in terms of b.

`\begin{gathered} b\tan 25^(\circ)-b\tan 16^(\circ)=35 \\ b=(35)/(\tan 25^(\circ)-\tan 16^(\circ)) \\ =(35)/(0.1795) \\ =194.98 \\ \approx195 \end{gathered}`

The distance for the Macros standing from foot of tree is 195 ft.