Question

Two pillars are of equal height on either sides of a road, which is 100 m wide. The angles of elevation of the top of the pillars are 60° and 30° at a point on the road between the pillars. Find the position of the point between the pillars and height of each pillar

Answer 1

Let AB and ED be two pillars each of height h metres. 

Let C be a point on the road BD such that BC = x metres. 

Then, CD = (100 – x) metres Given, ∠ACB = 60° and ∠ECD = 30°

In ΔABC, tan 60° = \(\frac{AB}{BC}\)

⇒ √3 = \(\frac{h}x\) ⇒ h = \(\sqrt3x\)            ..........(i)

In ΔECD, tan30° = \(\frac{ED}{CD}\)

⇒ \(\frac{1}{\sqrt3}=\frac{h}{100-x}⇒h\sqrt3 = 100-x\)          ..........(ii)

∴ Subst. the value of h from (i) in (ii) , we get

\(\sqrt3x.x\) = 100 - x ⇒ 3x = 100 - x ⇒ 4x = 100 ⇒ x = 25m

∴ h = (\(\sqrt3\) x 25)m = 25 x 1.372 m =  43.3m

∴ The required point is at a distance of 25 m from the pillar B and the height of each pillar is 43.3 m.