Let the height of the smaller pillar be h meters

Then, the height of the taller pillar is 3h meters

Let M be the midpoint of the line joining the feet of the two pillars

Since M is the midpoint, the horizontal distance from M to each pillar is:

AM = CM = \frac{150}{2} = 75 meters

Let the angles of elevation from M to the tops of the two pillars be θ and 90° – θ, since they are complementary.

In Δ MCD,

tan θ = \frac{h}{75}

In Δ AMB,

tan (90° – θ) = \frac{3h}{75}

⇒ cot θ = \frac{3h}{75}

⇒ \frac{1}{\tan θ} = \frac{3h}{75}

⇒ 75 = 3h tan θ

⇒ 25 = h tan θ

⇒ 25 = h \frac{h}{75}

⇒ h² = 25 × 75 = 1875

⇒ h = 25 √3 m

∴ Height of the smaller pillar = 25 √3 m