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