Question

Triangle ABC is an equilateral triangle, whose side is 2a. Find its height?​

Answer 1

we construct a perpendicular bisector AD

now, triangle abd

(2a)^2= (a^2) + (ad)^2

4a^2-a^2=ad^2

3a^2=ad^2

a√3=ad (height)

Answer 2

Step-by-step explanation:

If length of 1 side = 2a

Half the length of base = a [as median bisects the base i.e., AD bisects BC]

We know that,

sin(A) = hypotenuse/opposite side

Also in an equilateral triangle all angles are 60°.

•°•sin60=AC/AD

(3^1/2)/2=2a/AD

(3^1/2)AD = 4a

AD = 4a/(3^1/2)

$ad = \frac{4a}{ \sqrt{3} }$