Answer:
51 units
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
short leg : long leg : hypotenuse = 1 : sqrt(3) : 2
The reason this is relevant here is that in your case, you start with an equilateral triangle, FGH. An equilateral triangle is also equiangular, so all angles are congruent and measure 60 deg.
m<F = m<FGH = m<H = 60 deg
When the height GR is drawn, <FGH is bisected creating two 30-60-90 degree triangles, FGR and HGR.
The altitude GR also bisects side HF, so
HR = FR = (1/2)HF = 17*sqrt(3)
In 30-60-90 degree triangle FRG, the short leg is FR; the long leg is GR; the hypotenuse is FG.
Now we use the ratio of the lengths of the sides of a 30-60-90 degree triangle.
short leg : long leg : hypotenuse = 1 : sqrt(3) : 2
We use only the short leg and long leg parts of the ratios.
17*sqrt(3) : GR = 1 : sqrt(3)
GR * 1 = 17 * sqrt(3) * sqrt(3)
GR = 17 * 3
GR = 51
