How do i calculate the height of an equilateral triangle - top 60 and side 7m?

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Answer 1 · 2018-04-04T15:26:34

#color(blue)((7sqrt(3))/2m)#

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By definition of an equilateral triangle:

#ABC#

#AB=BC=AC#

#/_ABC=/_BCA=/_CAB#

So for given triangle:

All sides = 7m

All angles = #60^@#

Taking a perpendicular bisector DC.

This is the altitude of the triangle, which is what we require.

Using triangle BCD

#/_CBD=60^@#

#sin(/_CBD)=sin(60)="opposite"/"hypotenuse"=(DC)/7#

#=>DC=7sin(60)=color(blue)((7sqrt(3))/2m)#