## anonymous 4 years ago i need help solving a triangle with a Angle of 39.4 degrees there are 2 sides the longest side is 7.11 and a leg that is 3.56 i have to find the side opposite the 39.4 degree angle and the angles that correspond with the 2 sides

1. Hero

You see that draw button? You should click that and try to create the triangle.

2. anonymous

|dw:1327274366132:dw| this is what it looks like

3. Hero

Apply law of Cosines

4. anonymous

which is $\sqrt{b ^{2}+c ^{2}-ABcos(\theta)}$right

5. Hero

Make sure it is right

6. anonymous

BCcos(theta)*** sorry

7. anonymous

no.. use a^2 = b^2 + c^2 - 2*b*c*cos(A)

8. anonymous

oh did i miss the 2?

9. anonymous

bingo x

10. anonymous

thats what is throwing me off

11. anonymous

thank you both

12. phi

and use the law of sines to find the angles.

13. anonymous

im convinced that im doing everything right but i cannot seem to get the right answer, i know this because i can not get the interior angles to equal 180 degrees

14. phi

what did you get for the 3rd side?

15. anonymous

4.91

16. phi

A to scale picture might help here |dw:1327279521199:dw|

17. phi

notice that the angle opposite 7.11 is quite large. Also, notice that sin A = x can have 2 answers symmetric about 90º (actually an infinite number of answers if we keep going... but only 2 within 180º)

18. anonymous

yes i see that

19. phi

so find the "other angle"

20. phi

if you found A find 90 + (90-A) = 180-A

21. anonymous

i used the law of sines and computed 7.11sin(39.4)/4.91 in my calculator but i took the inverse sin of the that

22. phi

and got?

23. anonymous

66.80

24. anonymous

and i repeated for the final angle and got 27.4

25. phi

but for the angle opposite side 7.11, 66.8 is too small. Find the *other angle* which is 180-A, or 180-66.8

26. anonymous

well that should be 78 degrees but im getting 27.4

27. phi

I am not being clear, am I? Your 39.4 and 27.4 are correct. the problem is your 66.8 is not correct. You did it right (take the inverse sin of 7.11sin(39.4)/4.91 but notice that there is another angle that has exactly the same sin (see picture up above) that angle is at 180-66.8

28. anonymous

ohhhhhhhh

29. phi

The only way to know which angle to choose is to notice that one of the angles is obtuse (greater than 90º) You found one way to notice... the angles did not add up to 180º so the culprit is the angle opposite the longest side, because that will be the largest angle

30. anonymous

okay ya that makes sense

31. anonymous

thank you so very much

32. phi

yw