Question

which set of values could be the side lengths of a 30-60-90 triangle?
A. (6, 12, 12 square root 3)
B. (6, 12, 12 square root 2)
C. (6, 6 square root 2, 12)
D. (6, 6 square root 3, 12)

Answer 1

Any triangle having one of the three angles as 90 is a right angled triangle.
All right angled triangles obey Pythagoras theorem. hypotenuse\[hypotenuse ^{2} = side1^{2}+side2^{2}\] .
Side opposite to 90 degree angle is called hypotenuse and it will be the longest side in the triangle.
So applying these rules..
\[12^{2} = 6^{2} + (6\sqrt{3})^{2}\]
Reason: 12 is the longest length side among the given sides, so it should be hypotenuse. Applying Pythagoras theorem

Answer 2

{6,6sqrt3,12}