Which THREE pairs of measurements are possible side lengths for a 30-60-90 triangle? C= 30, B = 90, A = 60

1. AB+4, BC = 4√3
2. 2√3, AC = 2
3. AB = 3, AC = 3√3
4. BC = 10, AC = 4√3
5. AB = 7, AC = 14
6. AB = 11, BC = 11√3

1, 5 and 6.

Step-by-step explanation:

The sides of this triangles has lengths in the ratio x : √3x : 2x where 2x is the hypotenuse.

When C = 30,  the side AB is the small leg  (=x).

When B = 90, the hypotenuse is  AC ( =2x).

When A =  60, the larger leg is BC (=√3x).

1.  AB = 4, BC = 4√3 :- Are possible legs.

5 AB = 7, AC = 14. :-  AB = small leg, AC = hypotenuse.

6. AB = 11, BC = 11√3:-   AB = small, BC = larger leg.

the correct is answer is a 9-sided polygon!

think about it deeply and passionately about this property

i am sorry