meg1334 2 years ago will give medal to best answer! The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. C = 38°, a = 19, c = 10

1. Hero

Did you try simply using Law of Sines to figure it out?

2. meg1334

yes but i didnt understand

3. Hero

What did you come up with?

4. meg1334

i got sin A = 67 but that isnt in my answer choices No triangle is formed. A = 58.6°, B = 83.4°, b ≈ 15.6 A = 83.4°, B = 58.6°, b ≈ 15.6 The triangle cannot be solved with the Law of Sines.

5. Hero

I don't understand how you got that. Please show me the steps you took to get A = 67

6. meg1334

i used c/ sin c = a/ sin a 10/sin 37 = 19/sin a and then i divided 19 sin 38 over sin 10 and i got 67.36

7. Hero

where did you get the 37 from?

8. meg1334

I meant 38, i used 38 in my claculations and still got 67

9. meg1334

calculations

10. Hero

Are you in degree mode or radian mode?

11. meg1334

i dont know i just typed it in and got 67, cant you check it?

12. Hero

You must make sure you're in degree mode. That's very important.

13. Hero

But either way it goes, you're not doing it correctly.

14. meg1334

oh really, i hadnt noticed that im doing it wrong. I need help thats why im on here obviously

15. Hero

$\sin A = \frac{19\sin(38^{\circ})}{10} \\\sin A =$

16. Hero

Compute the right hand side again and let me know what you get. Make sure you're in degree mode.

17. meg1334

1.169756803

18. Hero

Okay now $\sin A = 1.169756803$ So how do we find A?

19. meg1334

a is 19, sin A is 1.16, what do you mean find A?

20. Hero

A is an angle. Find it

21. Hero

A is an Angle like theta

22. Hero

I'm not talking about a = 19. That's a side length

23. Hero

$\sin (A^{\circ}) = 1.169756803$ I'm talking about Angle A. Find that.

24. meg1334

how?

25. Hero

You take the inverse sine of both sides to get: $\sin^{-1}(A^{\circ}) = \sin^{-1}({1.169756803}) \\A^{\circ} = \sin^{-1}({1.169756803})$

26. Hero

So compute $\sin^{-1}({1.169756803})$

27. Hero

Let me know what you get.

28. meg1334

it says error

29. Hero

Exactly.

30. Hero

That's what it should say because no such angle exists.

31. Hero

And if the angle doesn't exist, then the triangle can't possibly exist.

32. Hero

$-1< \sin(\theta) < 1$ means that the value of sine can only be between - or + one. So there's no such thing as $$\sin(\theta) = 1.17$$