what is the height of an equilateral triangle with an area of 43.3?

We can calculate this by first finding a side length, s ....we have

43.3 = (1/2) s^2 (sin 60)  =

43.3 = (1/2) s^2 (√3/2)      mutiply both sides by 4/√3

(43.3)(4/√3) = s^2        take the square root of both sides

s = about 10

So the altitude is (10/2)√3  = 5√3  = about 8.66 linear units

Check......  (1/2)bh = (1/2)(10)(5√3)  = about 43.3