## TNNG 2 years ago Solve the triangle. B = 36°, a = 41, c = 20

1. TNNG

b ≈ 27.5, C ≈ 115.5, A ≈ 28.5 b ≈ 45.3, C ≈ 25.5, A ≈ 118.5 b ≈ 45.3, C ≈ 29.5, A ≈ 114.5 b ≈ 27.5, C ≈ 25.5, A ≈ 118.5

2. terenzreignz

Law of Cosines?

3. geerky42

Yes.

4. terenzreignz

You arrived at a solution, @TNNG ?

5. geerky42

Use law of cosines to find b then use law of sines to find the rest of angles.

6. TNNG

ok so just use to law of cosines and i should get the answer

7. geerky42

Well, you're not finished, since you still have to find A and C so use law of sines for this.

8. TNNG

i don't get it i got the D for my answer is that correct

9. geerky42

What don't you get?

10. TNNG

the law of sines

11. geerky42

The Law of Sines: $$\Large \dfrac{\sin A}{a} =\dfrac{\sin B}{b} =\dfrac{\sin C}{c}$$

12. geerky42

Familiar with it?

13. TNNG

i know that but i don't get how to plug it is plus i tried it again and got Choice B

14. terenzreignz

Well, you could certainly use the law of Cosines to arrive at all the other missing parts of the triangle, but that's really cumbersome, compared to the simpler looking law of sines.

15. geerky42

Yeah, it's only way to find the b. You just have to use it once, then use law of sines and you're good to go. You don't have to use entire formula, just use part of it, like $$\dfrac{\sin B}{b} = \dfrac{\sin C}{c}$$ Is this clear?

16. geerky42

The law of tangents is really cumbersome compared to the law of cosines :P

17. TNNG

ok so i know b=27.5

18. geerky42

Yes.

19. TNNG

so figure out that a = 28.5

20. geerky42

No, no, you already have the given value of a, so just use law of sines to find the angle.

21. geerky42

Now you know a, b, c, and B. Now all you need to do is find A and C.

22. TNNG

is the angle 25.5

23. geerky42

None, not what I get.

24. TNNG

115.5

25. pooja195

b^2 = a^2 + c^2 - 2accosB b = 27.5

26. geerky42

Wait, you're right, angle C is close to 25.5º. My bad. Now find the other angle.

27. geerky42

180º - (A + C) = B

28. TNNG

118.5

29. TNNG

so i had it right the first time

30. geerky42

Yes! Is this clear?

31. geerky42

You have to do math, though. You can't just guess. Just saying.