Question

What is the long leg of a 30 60 90 triangle when the hypothesis is 8 root 6

Answer 1

I will call the short side s and the hypotenuse h.

The sine rule states that in any triangle, the length of any side divided by the sine of the opposite angle is a constant.

So for your triangle we have:

8/sin 60° = s/sin 30° = h/sin 90°

8/[(sqrt 3)/2] = s/(1/2) = h/1

16/sqrt 3 = 2s = h

So the length of the short leg s

= 8/sqrt 3 = approx. 4.619

and the length of the hypotenuse

= 16/sqrt 3 = approx. 9.238.