When I work out x I get 2 different answers. Wondering if someone can explain?

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- Aug 3rd 2006, 07:30 AMclassicstringsWeird Question Different Answers?
When I work out x I get 2 different answers. Wondering if someone can explain?

- Aug 3rd 2006, 07:42 AMCaptainBlackQuote:

Originally Posted by**classicstrings**

RonL - Aug 3rd 2006, 07:45 AMclassicstringsQuote:

Originally Posted by**CaptainBlack**

- Aug 3rd 2006, 08:31 AMQuickQuote:

Originally Posted by**classicstrings**

- Aug 3rd 2006, 08:33 AMCaptainBlackQuote:

Originally Posted by**classicstrings**

and the parallel lines are, and the lengths are as indicated, then your angle

marked as 50 degrees will in fact be more like 40 degrees, ie the data you

have been given is inconsistent, so of course you get different answers

depending on how you calculate things.

RonL - Aug 3rd 2006, 09:37 AMtopsquarkQuote:

Originally Posted by**Quick**

-Dan - Aug 3rd 2006, 11:38 AMSoroban
Hello, classicstrings!

The diagram is quite impossible . . . They**lied**to us!Code:`C`

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b=4 * * a

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* 60° *

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A c=6 B

Law of Cosines: .$\displaystyle a^2\:=\:b^2 + c^2 - 2bc\cos A$

We have: .$\displaystyle a^2\:=\:4^2 + 6^2 - 2\cdot4\cdot6\cos60^o\:=$ $\displaystyle \:28\quad\Rightarrow\quad a \,= \,\sqrt{28} \,= \,2\sqrt{7}$

Law of Sines: .$\displaystyle \frac{\sin B}{b}\,=\,\frac{\sin A}{a}$

We have: .$\displaystyle \frac{\sin B}{4}\,=\,\frac{\sin60^o}{2\sqrt{7}}\quad \Rightarrow\quad \sin B \:=\:\frac{4\sin60^o}{2\sqrt{7}}\:=\:0.654653671$

Therefore: .$\displaystyle B\;=\;\sin^{-1}(0.654653671)\:=\:$ $\displaystyle 40.839339654 \quad\Rightarrow\quad B \:\approx \:41^o$

See? . . . and*they*told us that $\displaystyle B\,=\,50^o$