## anonymous 5 years ago tan∠A - csc∠C = 3x

1. anonymous

How do you solve this?

2. anonymous

At some point I got 3x sqrt74/5= 7/sqrt 74

3. anonymous

i am confused because you have 3 variables, A, C and x. what are you trying to solve?

4. anonymous

I am solving for this :tan∠A - csc∠C = 3x

5. anonymous

here are the variables

6. anonymous

tangent A= 7/sqrt 74 and csc C= sqrt74/5

7. anonymous

Hello?

8. anonymous

idk what you are saying

9. anonymous

Its tangent a subtracted from cosecant C and those are the values of them

10. anonymous

What the bannana are you talking about?

11. anonymous

haha

Wait, I'm confused. So you have: $\tan A - \csc C = 3x$ And: \begin{align} \tan A &= \frac{7}{\sqrt{74}}\\ \csc C &= \frac{\sqrt{74}}{5} \end{align} Right?

14. anonymous

Yes that is right

Ok, so you really have: $\frac{7}{\sqrt{74}} - \frac{\sqrt{74}}{5} = 3x$

16. anonymous

Yes exactly

First things first, I would do the subtraction on the left. Do you know how to do that?

18. anonymous

do you subtract the square?

19. anonymous

So, 3x = -39/(5*SQRT(74)) => x = -13/(5*SQRT(74))

20. anonymous

did you use the values GT?

21. anonymous

I am kind of shaky on how to subtract with squares shadowfield

22. anonymous

|dw:1326987711543:dw|

23. anonymous

|dw:1326987783481:dw|

You can make the denominators the same by multiplying each fraction by the other fraction's denominator:  \begin{align} \frac{7}{\sqrt{74}} &- \frac{\sqrt{74}}{5}\\ \frac{5}{5}\frac{7}{\sqrt{74}} &- \frac{\sqrt{74}}{\sqrt{74}}\frac{\sqrt{74}}{5}\\ \frac{35}{5\sqrt{74}} &- \frac{74}{5\sqrt{74}}\\ \end{align} So you get: $\frac{35 - 74}{5\sqrt{74}}$ GT has the rest of the work :)

25. anonymous

is that the simplified answer? Because I don't see it on my answer choices?

26. anonymous

|dw:1326988065164:dw|

27. anonymous

There are other ways to write it. What are the choices?

28. anonymous

74/15 , 7-5sqrt 74/5, 7-sqrt74/15 or 74/21

29. anonymous

Then, the ratios you gave for tan and csc must be wrong. Where did you get those from?

30. anonymous

|dw:1326988372290:dw|

31. anonymous

I first had to find the missing side then use the ratios

32. anonymous

What is A and B and C?

33. anonymous

Well, before I say that I found C by using the pythagorean therom and got sqrt 74?

34. anonymous

I understand and that is right. BTW - from the picture, I can already tell your Tan(a) is wrong. There is no hypotenuse involved in the tangent ratio.

35. anonymous

Ok wait... let me post the letters

36. anonymous

|dw:1326988584560:dw|

37. anonymous

Sorry for the messiness lol

38. anonymous

Good. Now, we can do it right. Tan A = BC/AB (opposite / adjacent) = 7/5 Csc C = AC/AB (hypotenuse / opposite) = SQRT(74)/5

39. anonymous

Now subtract and you will get the right answer.

40. anonymous

|dw:1326988606286:dw|

41. anonymous

That is equal to 3x. Now, x will be equal to 1/3 of that value.

42. anonymous

|dw:1326988707325:dw|

43. anonymous

So you multiplied both sides by 5?

44. anonymous

WOOHOOO!! Thank you so much I got a 100!

45. anonymous

Thanks everyone

46. anonymous

Great. Hope you also now can solve such problems with ease!

47. anonymous

I do to lol!