Help with quick math prob please - 10 points

There is a right triangle whose other two angles are 60 degrees and 30 degrees. The hypotenuse length is 12 inches. What are the lengths of the legs?

I'm pretty sure you use trig here, and if so, this is what I have so far (x = unknown):

sine (60) = x/12

Any help?

Well, what you have is already good. That should give you one of the other legs. All you need to do is to cross-multiply the 12 to the sin (60) to get the other leg's measure.

sin (60) = x / 12
12 sin (60) = x
6 sqrt (3) = x

Now, to get the other leg, you will have to use cosine. So, if you set that leg's measure to y, you'll have

cos (60) = y / 12
12 cos (60) = y
6 = y

Now, you have the measure of your 2 legs.

Hope this helps!!!!

sin(60) =x/12
sin(60)*12 =x
(square root 3)/2 *12 =x (special triangle or calculator will get u the answer);
x=6 *(square root 3) or 10.39;

the other one is 6 because of a special triangle rule
or the hard way
cos(60) =z/12
cos(60) *12 =z (calculator or special triangles)
z=6

sin 60 = a /12
sin 30 = b /12

sin30 = 1/2 = b/12 then b = 6
sin 60 = (√3)/2 = a/12 then a = 6(√3)

triangle has 3 sides
hypothenuse c = 12 ; leg a =6(√3) ; leg b = 6