How do I turn a number into a degree? i am in pre-calculus, we are using the low of cosine to find the angles for a three (SSS) problem. i got the number but i don't get how they turned it into a degree. the answer is: .4815, but they then turn it into a degree of 61.2.... how?

Question

jhannybean · Answer

Like a radians to degrees conversion?

jhannybean · Answer

I'll give you an example, say you have $4\pi$

jennyrlz · Answer

Hmm I have to find the angles of the triangle with the given sides of a=8, b= 3 and c=9

jhannybean · Answer

To turn $4\pi$ into degrees you multiply $4\pi \cdot \dfrac{180^\circ}{\pi}$

jhannybean · Answer

Ok, can you draw our your triangle?

jennyrlz · Answer

I alredy drew it, and I have the answer I just can't turn the answer into degrees :/

jennyrlz · Answer

I used cosA=(b^2+c^2-a^2)/2bc

jennyrlz · Answer

And got .4815 but how do I turn this into degrees?

jennyrlz · Answer

The book got 61.2 degreees but I do not know how they got this >.<

jhannybean · Answer

law of cosines: $a^2 = b^2 +c^2 -2bc\cos(A) \implies \cos(A) = \dfrac{a^2-(b^2+c^2)}{-2bc}$ where $a=8~,~ b = 3~,~ c = 9$

Right?

jhannybean · Answer

Oh, I see, you distributed the negative sign.

jennyrlz · Answer

My book has cosA=b^2+c^2-a^2 over 2bc

jhannybean · Answer

Yeah, i didnt completely simplify, I guess that would make it a little different.

jhannybean · Answer

$$a^2 = b^2 +c^2 -2bc\cos(A) \implies \cos(A) = \dfrac{-a^2+(b^2+c^2)}{2bc}$$$$a=8~,~ b= 3~,~ c = 9$$Plugging these values in I also get $\cos(A) \approx 0.48148$

jhannybean · Answer

Now to get the angle $A$,, you need tot ake the inverse cosine of the function.

jhannybean · Answer

that means, $\cos^{-1}(0.48148) = A$

jhannybean · Answer

Setting your calculator in degree mode, and calculating $\cos^{-1}(\#) $, you should get $\approx 61.2^\circ$`

jennyrlz · Answer

Hmm  I got 28.78 degrees

jennyrlz · Answer

Oh never mind I plugged it in wrong thanks a bunch :D!!!

jhannybean · Answer

No problem :)

jennyrlz · Answer

This is my first time using this website :D, I should come more often!

jhannybean · Answer

yeah! Of course :D This place has really helpful people that help you understand a bunch of questions using various techniques

jennyrlz · Answer

Thanks again (((o(*ﾟ▽ﾟ*)o)))

jhannybean · Answer

No problem :)

jennyrlz · Answer

Does this just stay open or am I supposed to close it 0.o

jhannybean · Answer

If your question is complete or if you'd like to ask another one, then you should close this one and post up a new question in a new thread :)

jennyrlz · Answer

Alright, thanks again :p