## briana.img one year ago How to find the angle measure of T?

1. briana.img

I have no idea how to solve this since there's no other angle measure

2. anonymous

Try the law of cosines. Do you know it?

3. wolf1728

Here is the Law of Cosines

4. briana.img

@wolf1728 are you sure thats it? i thought it was a^2=b^2+c^2-2bc cosa ???

5. anonymous

In your problem, let the three sides be t=7, r=11, s=10. Then the law of cosines becomes$t ^{2}=r ^{2}+s ^{2}-2rs \cos \left( T \right)$

6. wolf1728

ospreytriple's equation is better to use because itis written in terms of r, s and t

7. briana.img

@ospreytriple would i just plug in the numbers from the triangle???

8. anonymous

Rearranging, you get$T=\cos ^{-1}\left(\frac{ r ^{2} +s ^{2}-t ^{2}}{ 2rs }\right)$

9. briana.img

@ospreytriple i'm really confused on how i would get a real answer out of that equation :(

10. anonymous

just plug in the lengths of sides r, s, & t from the triangle.

11. briana.img

@ospreytriple oh okay that's what i was wondering lmao

12. anonymous

What do you get for an answer?

13. briana.img

@ospreytriple 45.57

14. anonymous

Not what I get. You want to try it again?

15. briana.img

@ospreytriple i got 63.25 :(

16. briana.img

@ospreytriple i got 63.25 :(

17. briana.img

@ospreytriple T=10? r=7? s=11?

18. anonymous

No. t=10. You are trying to find angle T.

19. wolf1728

briana r^2 = 121 s^2 = 100 t^2 = 49 r^2 + s^2 -t^2 = 172 agreed?

20. wolf1728

I think having 2 people explain things to a third gets a bit confusing good luck briana and osprey :-)

21. briana.img

@ospreytriple i listed those numbers because those are the ones you substitute in, right??

22. anonymous

Ok. Evaluate the above equation for T by using the values of r, s, & t from the triangle.

23. briana.img

@ospreytriple i know but i'm just asking if those are the numbers i use ??? like those are the correct ones for the substitution

24. anonymous

I believe those are the side lengths from the triangle, yes.

25. anonymous

$T=\cos ^{-1}\left( \frac{ 11^{2}+10^{2} -7^{2}}{ 2\left( 11 \right)\left( 10 \right) } \right)$

26. briana.img

@ospreytriple yeah i jsut did that and my answer came out to be 63.25 again

27. anonymous

What do you get for the value of the numerator?

28. briana.img

@ospreytriple 70

29. anonymous

Not quite.$11^{2}+10^{2}-7^{1}=121+100-49= ?$

30. anonymous

Should be 7^2. Sorry.

31. briana.img

@ospreytriple oh oops 172

32. anonymous

Great. Now the denominator is$2\left( 11 \right)\left( 10 \right)=?$

33. briana.img

@ospreytriple 220

34. anonymous

Terrific so$T=\cos ^{-1}\left( \frac{ 172 }{ 220 } \right)=?$

35. briana.img

@ospreytriple the calculator i'm using says 63.25???

36. briana.img

@ospreytriple wait nevermind 38.64

37. anonymous

Now you got it. Good job.

38. briana.img

@ospreytriple sorry fro taking so long :( this unit is really messing me up

39. anonymous

You're welcome. Those pesky calculators :)