Question

Two pillars of equal height stand on either side of a road way which is 60 m wide. At a point in the roadway between the pillars, the elevation of the top of the pillars are 60° and 30°.The height of the pillar is

(a) \(\frac{15}{\sqrt3}\) m

(b) 15 m

(c) \(15\sqrt3\) m

(d) 20 m

Answer 1

(c)  15\(\sqrt3\) m

Let PQ and RS be the two pillar of equal height = h metres (say)

Given,

T is a point on the line joining the bases of PQ and RS such that QT = x m (say),

then,

TS = (60 – x) m  (∵ QS = 60 m)

∠PTQ = 60°, ∠RTS = 30°,

In rt. Δ PQT,

tan 60° = \(\frac{PQ}{QT}\) 

⇒ \(\frac{h}{x}=\sqrt3\) 

⇒ x = \(\frac{h}{\sqrt3}\)  ...(i)

In rt. Δ RTS,

tan 30° = \(\frac{RS}{TS}\)

⇒ \(\frac{h}{60\,-\,x}=\frac{1}{\sqrt3}\)

⇒ x = 60 - \(\sqrt3h\)  ...(ii)

From (i) and (ii),

\(\frac{h}{\sqrt3}=60-\sqrt3h\)

⇒ 4h = 60\(\sqrt3\) 

⇒ h = 15\(\sqrt3\) m.