We have triangle with $A B = 6, ˆ A = \frac{π}{3} and ˆ B = \frac{π}{4}$ $AB=6,hat(A)=pi/3 and hat(B)=pi/4$ .How to find $A C and B C$ $AC and BC$ ?

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We have triangle with $A B = 6, ˆ A = \frac{π}{3} and ˆ B = \frac{π}{4}$ $AB=6,hat(A)=pi/3 and hat(B)=pi/4$ .How to find $A C and B C$ $AC and BC$ ?

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Answer 1 · 2017-04-22T00:20:50

See below.

Explanation:

Using the so called sinus law.

$\frac{sin ˆ C}{A B} = \frac{sin ˆ A}{B C} = \frac{sin ˆ B}{A C}$ $(sin hat C)/[AB] = (sin hat A)/[BC] = (sin hat B)/[AC]$

but

$ˆ A + ˆ B + ˆ C = π$ $hat A + hat B + hat C = pi$ and

$ˆ A = \frac{π}{3}$ $hat A = pi/3$
$ˆ B = \frac{π}{4}$ $hat B = pi/4$

so

$ˆ C = π - \frac{π}{3} - \frac{π}{4} = \frac{5 π}{12}$ $hat C = pi -pi/3-pi/4 = (5pi)/12$

and now

$B C = A B (\frac{sin ˆ A}{sin ˆ C}) = 6 ⎛ ⎜ ⎝ \frac{sin (\frac{π}{3})}{sin (\frac{5 π}{12})} ⎞ ⎟ ⎠ =$ $BC= AB( (sin hat A)/(sin hat C)) = 6(sin(pi/3)/sin((5pi)/12))=$
$9 \sqrt{2} - 3 \sqrt{6}$ $9sqrt2-3sqrt6$

and also

$A C = 6 ⎛ ⎜ ⎝ \frac{sin (\frac{π}{4})}{sin (\frac{5 π}{12})} ⎞ ⎟ ⎠ =$ $AC = 6 (sin(pi/4)/sin((5pi)/12))=$
$6 \sqrt{3} - 6$ $6sqrt3-6$

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We have triangle with $A B = 6, ˆ A = \frac{π}{3} and ˆ B = \frac{π}{4}$ $AB=6,hat(A)=pi/3 and hat(B)=pi/4$ .How to find $A C and B C$ $AC and BC$ ?

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Explanation:

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We have triangle with AB=6,ˆA=π3andˆB=π4AB=6,hat(A)=pi/3 and hat(B)=pi/4.How to find ACandBCAC and BC?

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Explanation:

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We have triangle with $A B = 6, ˆ A = \frac{π}{3} and ˆ B = \frac{π}{4}$ $AB=6,hat(A)=pi/3 and hat(B)=pi/4$ .How to find $A C and B C$ $AC and BC$ ?