Question

Please help! 10 points, serious answers!

Answer 1

So with this triangle, it's considered a "special triangle". The 30-60-90 triangle states that if the short leg is x, the hypotenuse is 2x and the long leg is x√3.

Now since the 60° is across from 11, I can presume that 11 is the long leg, and to get the short leg HG, you would need to divide 11 by √3. However, we need to rationalize the denominator. To do that, multiply the fraction by √3/√3:

$\frac{11}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}=\frac{11\sqrt{3}}{3}$

Next, since we got the short leg, multiply that by 2 to get the hypotenuse:

$\frac{11\sqrt{3}}{3}\times\frac{2}{1}=\frac{22\sqrt{3}}{3}$

In short, HG = $\frac{11\sqrt{3}}{3}$ and HI = $\frac{22\sqrt{3}}{3}$ . The correct option is D.