Asked by Anonymous
                What is the length of an equilateral triangle whose altitude has a length of 21
            
            
        Answers
                    Answered by
            Reiny
            
    Let each side be 2x
then we would have a right-angled triangle with sides, x, 21, and 2x so that
x^2 + 21^2 = (2x)^2
3x^2= 441
x^2 = 147
x = √147 = 7√3
so each side of the equilateral triangle is 14√3
or using trig
let each side be s
then 21/s =sin60°
s = 21/sin60° = 21/(√/2) = 42/√3
= 14√3 after rationalizing the denominator, same asnwer as above.
    
then we would have a right-angled triangle with sides, x, 21, and 2x so that
x^2 + 21^2 = (2x)^2
3x^2= 441
x^2 = 147
x = √147 = 7√3
so each side of the equilateral triangle is 14√3
or using trig
let each side be s
then 21/s =sin60°
s = 21/sin60° = 21/(√/2) = 42/√3
= 14√3 after rationalizing the denominator, same asnwer as above.
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