Question

When a eucalyptus tree is broken by strong wind its top strikes the ground at an angle of ${30}^{\circ }$ to the ground and at a distance of $15$ m from the foot. What is the height of the tree?

• A. $15\sqrt{3}m$
• B. $10\sqrt{3}m$
• C. $20$ m
• D. $10$ m

Answer 1

The correct option is A $15\sqrt{3}m$

From $\Delta ABC$

$\tan {30}^{\circ }=\frac{x}{15}$

$\frac{1}{\sqrt{3}}=\frac{x}{15}$

$x=\frac{15}{\sqrt{3}}$

$x=5\sqrt{3}$

By Pytagorous therom

$y^2=x^2+{15}^2$

$y^2=(5\sqrt{3}{)}^2+225$

$y^2=75+225$

$y^2=300$

$y=\sqrt{300}$

$y=10\sqrt{3}$

Height of tree is $5\sqrt{3}+10\sqrt{3}$

$⟹15\sqrt{3}$