Question

If the distance between the top of two trees of height 20 m and 28 m is 17 m, then the horizontal distance between the trees is:

• A. 11 m
• B. 31 m
• C. 15 m
• D. 9 m

Answer 1

The correct option is C

15 m

Let $AB$ and $CD$ be two trees such that $AB=20m,CD=28m\text{and}BD=17m.$

Draw a line $BE$ parallel to $AC$.
Then, $ED=8m$.

By applying Pythagoras' theorem in triangle BDE, we get
$B{E}^2+D{E}^2=B{D}^2$.

$\therefore BE=\sqrt{{BD}^2-{DE}^2}=\sqrt{{\left(17\right)}^2-8^2}$
$=\sqrt{289-64}=\sqrt{225}=15m$

$\therefore AC=BE=15m$

So, the horizontal distance between the trees is 15 m.