## anonymous one year ago use the law of cosines to find the value of 2⋅3⋅4 cosθ

1. anonymous

@dan815

2. anonymous

@taramgrant0543664

3. anonymous

what do you mean by 2⋅3⋅4 cosθ You mean $\cos 2\theta\quad,\cos3\theta,\quad \cos3\theta$?

4. taramgrant0543664

Do you have a triangle that corresponds to this question?

5. anonymous

|dw:1438361201942:dw|

6. taramgrant0543664

This is the law c^2=A^2+b^2−2abcosC

7. anonymous

21

8. taramgrant0543664

4=16+9-2(4)(3)cosC 21=24cosC 0.875=cosC C= 28.96

9. anonymous

A. 24 B. 21 C. -24 D. -21

10. taramgrant0543664

I just understood the whole 2,3,4 thing and ya it is equal to 21 I just assume you had to solve for the angle

11. anonymous

so is it 21 then

12. taramgrant0543664

Yes it is

13. anonymous

thanks

14. anonymous

can you help me with another question please? @taramgrant0543664

15. taramgrant0543664

I can try!

16. anonymous

ok

17. anonymous

|dw:1438362470160:dw|

18. anonymous

true or false

19. anonymous

@taramgrant0543664

20. anonymous

nvm

21. anonymous

wrong problem

22. anonymous

Suppose a triangle has sides a, b, and c, and that a2 + b2 > c2. Let be the measure of the angle opposite the side of length c. Which of the following must be true? Check all that apply.

23. anonymous

A. cos < 0 B. cos > 0 C. is an acute angle. D. The triangle in question is a right triangle.

24. anonymous

@taramgrant0543664

25. taramgrant0543664

I'd like to think it would be D but I'm not certain

26. anonymous

27. anonymous

i think its a and d

28. anonymous

what do you think

29. taramgrant0543664

A and D that's what I'm thinking

30. anonymous

yup yup

31. anonymous

Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true?

32. anonymous

33. anonymous

A. b2 + c2 < a2 B. a2 + c2 > b2 C. a2 + c2 < b2 D. a2 + b2 < c2

34. anonymous

@taramgrant0543664

35. anonymous

i think it a @taramgrant0543664

36. taramgrant0543664

Ya I was trying to think it out and I was thinking it was A but I was testing out the other options too to double check

37. anonymous

that good

38. anonymous

it wasnt a

39. anonymous

its aight

40. phi

Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true? they tell you about angle B (opposite side b) is bigger than 90 degrees (i.e. obtuse) I would write down the law of cosines in the form that uses angle B (because that is the angle we know about) b^2 = a^2 + c^2 - 2 a c cos B next, we (should!) know cos of an angle bigger than 90 (but less than 180) is negative in other words - 2 ac cos B will turn into a positive number (because -2 * neg cos will be positive) in other words, we can say b^2 = a^2 + c^2 + more if we subtract off more from the right side, the right side will no longer be equal to the left side ... it will be too small. we can say b^2 > a^2 + c^2 or (means the same thing) a^2 + c^2 < b^2