Question

Example 7. Two pillars of equal height and on either
side of a road, which is 80m wide. The angles 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 he road BD such that

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

$In ΔABC,tan {60}^{0} = \frac{AB}{BC} ⇒ \sqrt{3 } = \frac{h}{x} ⇒h= \sqrt{3} ...(i)$

$In ΔECD,tan {30}^{0} = \frac{ED}{CD}⇒ \frac{1}{ \sqrt{3} } = \frac{h}{100 - x} ⇒100 - x...(ii)$

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

$\sqrt{3.x} = \frac{100 - x}{ \sqrt{3} } ⇒3x=100−x⇒4x=100⇒x=25m</p><p></p><p>$

$∴ h=( \sqrt{3} ×25)=25×1.732m=43.3m$

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