0 votes
114 views
in Pythagoras theorem by (98.9k points)
edited
Find the height of an equilateral triangle having side 2a.

1 Answer

0 votes
by (98.9k points)
selected by
 
Best answer

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 = \(\frac{\sqrt{3}}{2}\) AB [Side opposite to 60°]
= \(\frac{\sqrt{3}}{2}\) × 2a
= a\(\sqrt { 3 }\) units
The height of the equilateral triangle is a\(\sqrt { 3 }\) units.

Related questions

0 votes
1 answer 227 views

Doubtly is an online community for engineering students, offering:

  • Free viva questions PDFs
  • Previous year question papers (PYQs)
  • Academic doubt solutions
  • Expert-guided solutions

Get the pro version for free by logging in!

5.7k questions

5.1k answers

108 comments

554 users

...