Question

Find the height of an equilateral triangle having side 4 cm?

Answer 1

Let ∆ABC be the given equilateral triangle.

∴ ∠B = 60°      ......[Angle of an equilateral triangle]

Let AD ⊥ BC, B – D – C.

In ∆ABD, ∠B = 60°, ∠ADB = 90°

∴ ∠BAD = 30°      ......[Remaining angle of a triangle]

∴ ∆ABD is a 30° – 60° – 90° triangle.

∴ AD = `sqrt(3)/2` AB    ......[Side opposite to 60°]

= `sqrt(3)/2 xx 4`

= `2sqrt(3)` units

∴ The height of the equilateral triangle is `2sqrt(3)` units.