tan∠A - csc∠C = 3x

- anonymous

tan∠A - csc∠C = 3x

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- anonymous

How do you solve this?

- anonymous

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

- anonymous

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

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## More answers

- anonymous

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

- anonymous

here are the variables

- anonymous

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

- anonymous

Hello?

- anonymous

idk what you are saying

- anonymous

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

- anonymous

What the bannana are you talking about?

- anonymous

haha

- shadowfiend

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?

- shadowfiend

jonh—please be respectful.

- anonymous

Yes that is right

- shadowfiend

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

- anonymous

Yes exactly

- shadowfiend

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

- anonymous

do you subtract the square?

- anonymous

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

- anonymous

did you use the values GT?

- anonymous

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

- anonymous

|dw:1326987711543:dw|

- anonymous

|dw:1326987783481:dw|

- shadowfiend

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 :)

- anonymous

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

- anonymous

|dw:1326988065164:dw|

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

|dw:1326988372290:dw|

- anonymous

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

- anonymous

What is A and B and C?

- anonymous

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

- 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.

- anonymous

Ok wait... let me post the letters

- anonymous

|dw:1326988584560:dw|

- anonymous

Sorry for the messiness lol

- 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

- anonymous

Now subtract and you will get the right answer.

- anonymous

|dw:1326988606286:dw|

- anonymous

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

- anonymous

|dw:1326988707325:dw|

- anonymous

So you multiplied both sides by 5?

- anonymous

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

- anonymous

Thanks everyone

- anonymous

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

- anonymous

I do to lol!

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