## IloveCharlie Group Title A triangular metal frame has sides 8 feet, 12 feet, and 16 feet. Find the measure of the largest angle between any two sides of the frame. The cosine of the largest angle=? 2 years ago 2 years ago

1. sasogeek Group Title

do you know the cosine rule?

2. IloveCharlie Group Title

Can you tell me it again? I forgot it

3. Nickv_1 Group Title

4. IloveCharlie Group Title

Thanks @Nickv_1 So @sasogeek I just use that?

5. Nickv_1 Group Title

welcome

6. sasogeek Group Title

we're not exactly sure if it's a right angled triangle, so we can't also conclude that it's adjacent over hypotenuse.... where is the adjacent, and where is the hypotenuse?

7. sasogeek Group Title

see, the cosine rule says that if you have a triangle, |dw:1344729963224:dw| $$\huge cosA=\frac{b^2+c^2-a^2}{2bc}$$ we can substitute the values and solve for A (each angle) and see which one is the largest :) then we can find the cosine of that largest angle :)

8. sasogeek Group Title

let's say for example using this triangle, |dw:1344730155989:dw| $$\huge cosA=\frac{16^2+8^2-12^2}{2(16*8)}$$ we can solve for A by taking the cos inverse of the value on the right side of the equation.

9. IloveCharlie Group Title

"on the right side of the equation"?

10. sasogeek Group Title

yeah, every equation has 2 sides :) left side = right side | | | | $$cosA \ \ \ \ = \frac{16^2+8^2-12^2}{2(16*8)}$$

11. sasogeek Group Title

so to find A, we find the cos inverse of the right side, like this... $$\huge A = cos^{-1}(\frac{16^2+8^2-12^2}{2(16*8)})$$

12. sasogeek Group Title

are we good to go?

13. IloveCharlie Group Title

I'm trying to solve. Just a sec

14. sasogeek Group Title

sure :)

15. IloveCharlie Group Title

I keep getting error when trying to solve using my TI83

16. sasogeek Group Title

hmm, let's see what i get..just a sec

17. sasogeek Group Title

angle A = 79.193 degrees :)

18. IloveCharlie Group Title

Thank you! So the final answer is 79.193?

19. sasogeek Group Title

no, you'll have to check the other angles to be sure which one is the largest :)

20. IloveCharlie Group Title

Oh o.k. So I use the same formula?

21. sasogeek Group Title

yeah :) i'll do it and tell you what i got, in the mean time, do it yourself and let me know what you got too :)

22. IloveCharlie Group Title

Sounds good

23. IloveCharlie Group Title

:)

24. sasogeek Group Title

sorry i made a mistake somewhere, A=46.567 B=104.478 C=28.955

25. IloveCharlie Group Title

Oh :/ Was it the formula or a mistake in the arithmetic?

26. sasogeek Group Title

i just miscalculated, the formula is correct though, the last answers i put up are right... did u get the same thing?

27. IloveCharlie Group Title

Yes, I used the formula :) So obviously B is the largest angle

28. sasogeek Group Title

:) so u got the largest angle, what are u supposed to do with it?

29. IloveCharlie Group Title

Take cosine. So just a sec... -.2500?

30. sasogeek Group Title

yay! :) our work is done here :)

31. IloveCharlie Group Title

And I couldn't have done it without you! Thank you so much I really appreciate it :)

32. sasogeek Group Title

anytime :) you're welcome :)