Question

Construct an equalateral triangle whose altitude is 6 cm

Answer 1

see the explanation

Explanation:

we know that

An equilateral triangle has three equal sides and three equal interior angles.

The measure of each interior angle is 60 degree

see the attached figure to better understand the problem

Let

b ----> the length side of the triangle

In the right triangle ABD

`sin(60^o)=(BD)/(AB)` ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

`sin(60^o)=(6)/(b)`

solve for b

`b=(6)/(sin(60^o))`

Remember that

`sin(60^o)=(√(3))/(2)`

substitute

`b=(6)/((√(3))/(2))`

`b=(12)/(√(3))\ cm`

simplify

`b=4√(3)\ cm`