## Life 3 years ago In triangle ABC, measure of angle A=33, a=12,b=15, what is the measure of angle b to the nearest degree?

1. Life

@geoffb

2. geoffb

Are you given a diagram? You should be able to use sin, cos, or tan to find angle B, since you know two sides (a and b).

3. geoffb

|dw:1353915380080:dw|

4. geoffb

Does it look like that?

5. geoffb

If so, use a rule like $$\tan B = \frac{15}{12}$$, though it might be different depending on your diagram.

6. Life

my diagram looks exactly like yours

7. geoffb

Perfect! You can solve for B using $$\tan^{-1} (\frac{15}{12})$$ then.

8. Life

i got a long decimal, although the choices im giveb are all whole numbers

9. geoffb

Okay, wait... If the triangle was a right-angle triangle, you could have solved for B by simply subtracting 90-33. So I imagine that's not the case. It's not a right-angle triangle, I'm guessing.

10. Life

wait, dont i use the law of sine?

11. geoffb

Yes.

12. Life

idk man do you know why i keep getting the decimal, all im doing is putting in the inverse of tan(15/12) into my calculator

13. geoffb

No, forget I said that. That was for a right-angle triangle. Like you said, you need to use the law of sines. $$\Large\frac{a}{\sin A} = \frac{b}{\sin B}$$ $$\Large\frac{12}{\sin 33} = \frac{15}{\sin B}$$

14. geoffb

$\sin B = \frac{15 \sin 33}{12}$

15. geoffb

Is 43 one of the possible answers?

16. Life

yea, so i dont find the inverse?

17. geoffb

Yes, you do. We got: $\sin B = \frac{15 \sin 33}{12}$ so... $B = \sin^{-1} (\frac{15 \sin 33}{12})$

18. Life

I see now, thanks out :D

19. geoffb

No problem. Have a good night. :)

20. Life

same for you :)