Consider the height of oak tree be x.
Determine the relation between oak tree height and distance B by using trigonometric ratio.
[tex]\begin{gathered} \tan 16^{\circ}=\frac{x}{b} \\ x=b\tan 16^{\circ} \end{gathered}[/tex]
Determine the relation between height of kite and distance B using the trigonometric ratios.
[tex]\begin{gathered} \tan 25^{\circ}=\frac{a}{b} \\ a=b\tan 25^{\circ} \end{gathered}[/tex]
The difference between height of kite (a) and height of oak tree (x) is 35 ft or,
[tex]a-x=35[/tex]
Substitute vaue a and x from the obtained to obtain the equation in terms of b.
[tex]\begin{gathered} b\tan 25^{\circ}-b\tan 16^{\circ}=35 \\ b=\frac{35}{\tan 25^{\circ}-\tan 16^{\circ}} \\ =\frac{35}{0.1795} \\ =194.98 \\ \approx195 \end{gathered}[/tex]
The distance for the Macros standing from foot of tree is 195 ft.
