Question

If you have a triangle with angles of 30, 60 and 90 with a side of 12, what would the other two sides be?

Answer 1

which side is 12?

Answer 2

side opposite 30 = 12?
side opposite 60 = 12?

or

side opposite 90 = 12?

these are 3 different results....

Answer 3

oops I wrote it wrong, the side opposite is 21

Answer 4

opposite 30

Answer 5

you can use the law of of sines or cosines to get the answer

Answer 6

law of sines is \[sineA/a=sinb/b\]

Answer 7

\[Sin 30/21=sine 60/x\]

Answer 8

cross multiply sin 30 x=(21)(sin60)

Answer 9

Use a calculator to figure out the sines
.05x = (21)(0.86602540378444)
x=9.09326673973662

Answer 10

so the side opposite 60 deg. is 9.09326673973662

Answer 11

if you can visualize the 30-60-90 triangle (or draw it); then things get simpler as well;

the slanted part(hypotenuse) has a normal value = 2

the leg opp. 60 has a normal value = sqrt(3)

the leg opp. 30 has a normal value = 1

since opp 30 = 21 in your problem, then 1x = 21..x = 21 we want to multiply all these "normal" values by 21 to get the measurements of the other 2 sides:

slant = 2(21) = 42

and leg opp 60 = 21sqrt(3) or 36.37

Answer 12

I messed up in the last part of the algebra