Problem
$d$ 10. Kyle and Anand are standing on level ground on opposite sides of a tree. Kyle measures the angle of elevation to the treetop as $35^{\circ}$. Anand measures an angle of elevarion of $30^{\circ}$. Kyle and Anand are $65 \mathrm{~m}$ apart. Kyle's eyes and Anand's eyes are $1.6 \mathrm{~m}$ above ground. How tall, to the nearest tenth of a metre, is the tree?
Solution
Step 1 ：Let the height of the tree be h, the distance from Kyle to the tree be x, and the distance from Anand to the tree be y. We have the following equations: \[\tan(35^\circ) = \frac{h - 1.6}{x}\] and \[\tan(30^\circ) = \frac{h - 1.6}{y}\] with x + y = 65.
Step 2 ：Solve the system of equations to find the height of the tree: \[h \approx 22.2 \text{ meters}\] \[\boxed{22.2}\]
