Question

If I am given a triangle with all 3 angles but only 1 side length how do I find the other sides?

Answer 1

trigonometric identities?

Answer 2

you can draw height to the triangle
then use basic trigonometry

Answer 3

Law of Sines

Answer 4

How do I use law of sines?

Answer 5

write the ratio of sin(A)/opposite side = sin(B)/opposite side

if we label the side opposite angle A as a, (i.e. use lower case letters for the sides) use
\[ \frac{\sin A}{a} = \frac{\sin B}{b} \]

Answer 6

Idk what to do after this:\[\frac{ \sin(83) }{ a }=\frac{ \sin(45) }{ b }=\frac{ \sin(52) }{ 12 }\]

Answer 7

just do one pair at a time
\[ \frac{ \sin(83) }{ a }=\frac{ \sin(52) }{ 12 } \]

one way is first cross multiply. can you do that ?

Answer 8

I got a = 15.08?

Answer 9

you should get
a= 12*sin(83)/sin(52)= 15.11

Answer 10

Okay yea I redid it and got that

Answer 11

I got 15.08 by rounding

Answer 12

ok, now do the other pair
\[ \frac{ \sin(45) }{ b }=\frac{ \sin(52) }{ 12 } \]

Answer 13

a=10.77

Answer 14

yes

Answer 15

Okay thank you!