## IloveCharlie 3 years ago 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=?

1. sasogeek

do you know the cosine rule?

2. IloveCharlie

Can you tell me it again? I forgot it

3. Nickv_1

4. IloveCharlie

Thanks @Nickv_1 So @sasogeek I just use that?

5. Nickv_1

welcome

6. sasogeek

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

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

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

"on the right side of the equation"?

10. sasogeek

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

11. sasogeek

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

are we good to go?

13. IloveCharlie

I'm trying to solve. Just a sec

14. sasogeek

sure :)

15. IloveCharlie

I keep getting error when trying to solve using my TI83

16. sasogeek

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

17. sasogeek

angle A = 79.193 degrees :)

18. IloveCharlie

Thank you! So the final answer is 79.193?

19. sasogeek

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

20. IloveCharlie

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

21. sasogeek

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

Sounds good

23. IloveCharlie

:)

24. sasogeek

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

25. IloveCharlie

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

26. sasogeek

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

27. IloveCharlie

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

28. sasogeek

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

29. IloveCharlie

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

30. sasogeek

yay! :) our work is done here :)

31. IloveCharlie

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

32. sasogeek

anytime :) you're welcome :)