## anonymous one year ago D(5, 7), E(4, 3), F(8, 2), form the vertices of a triangle . what is m<DEF ?

1. anonymous

30° 45° 60° 90° HELP 😩

2. anonymous

Plot it out on graph and use the distance formula to get the three sides and then you can use Cosine Law to figure out the angles.

3. anonymous

Have you learned about Cosine Law?

4. anonymous

No & I have no paper . I'm doing Plato .

5. anonymous

here is the graph:

6. anonymous

😵😵 where the points ? Or how do I read this graph 😨

7. anonymous

They did not give you a distance for none of the sides so to me it looks like you need to find the sides and use Cosine Law, which you can find the sides using he distance formula Here are your points https://www.desmos.com/calculator/zbzs1dzyyp

8. anonymous

I dont understand what the question means @Nixy, what is m<DEF?

9. anonymous

Measurement of angle DEF ?

10. anonymous

& I would type cos .... I'm confused

11. anonymous

sorry, normally slope is indicated by the letter m, so wasnt sure!

12. anonymous

need to explain rationale for using cosine law to @Jade3115

13. anonymous

I'm being timed 😩 so I'm going to have to guess

14. anonymous

Timed?

15. anonymous

I've spent 15 mins on one question .

16. anonymous

distance formula = $$\sqrt{(x_2 - x_1)^2+(y_2- y_1)^2}$$ D(5, 7), E(4, 3), F(8, 2) So from E(4,3) to D (5,7) $$\sqrt{(5 - 4)^2+(7- 3)^2}$$ That will give you the distance from E to D and that is one side.

17. anonymous

Who is timing you?

18. anonymous

The computer

19. anonymous

Do I pit cos before that ? @nixy

20. anonymous

Jade, there is a lot of work to do with this problem and to me you have to KNow about the distance formula and Cosine Law so this is going to take a little bit.

21. anonymous

Ugh. Thanks anyway .

22. anonymous

Do you understand the distance formula?

23. anonymous

No. I don't understand none of this stuf . That's why I'm doing this now

24. anonymous

why use the distance formula when answers are degrees?

25. anonymous

😂😂

26. anonymous

You need the sides to get the degree. ONce you have the sides you can use Cosine Law to get the degrees

27. anonymous

okay @Jade3115 is suggesting that the angle you are looking for is opposite one of the sides.|dw:1435458749504:dw|

28. anonymous

ha!, what @Jade3115 forgot to mention was that you were not given the lengths of the sides or any angles.

29. anonymous

Sorry, I am at work so I am in and out :-) @BPDlkeme234 That is why I suggested to her to use the distance formula first to find the sides and then she can use Cosine Law to find the angles

30. anonymous

I have just become a fan of @Jade3115 knowing where she was going with this.

31. anonymous

Once she has the the sides she can use formulas like the following to find the angles $\huge cos^{-1} E = \frac{b^2+c^2-a^2}{-2bc}$ To find the

32. anonymous

33. anonymous

But this solution obviously mean calculating the sides, as @Jade3115 said. Her solution was right.

34. anonymous

How was her solution correct? She did not have a solution. I am the one that told her she had to calculate the sides and then told her how and from there she has to use Cosine Law to figure the angles. The only solution she had was to guess at a random answer.