Question

The angle of elevation of the top of a tree of height 18 metres is 30° when measured from a point P in the plane of its base. The distance of the base of the tree from P is 

(a) 6 m

(b) 6√3 m

(c) 19 m

(d) 18√3 m

Answer 1

Correct option is (d) 18√3 m

Distance from tree = x

Length of tree = 18

Let the angle of elevation = 30^∘

Now, tanθ = \(\frac{\text{Length of tree}}{\text{Distance from tree}}\)

\(\tan 30° = \frac{18}x\)

\(\frac 1{\sqrt 3} = \frac{18}x \)

\(x = 18\sqrt 3\) m