A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ . If side C has a length of $25$ $25$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

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Answer 1 · 2016-07-02T14:26:21

$A = 25 (2 - \sqrt{3})$ $A=25(2-sqrt(3))$

you know, by the Euler theorem, that

$A : sin ˆ B C = C : sin ˆ A B$ $A:sin hat(BC)=C:sin hat(AB)$

so, in this case:

$A : sin (\frac{π}{12}) = 25 : sin (\frac{5 π}{12})$ $A:sin(pi/12)=25:sin((5pi)/12)$

by which you have:

$A = 25 \frac{sin (\frac{π}{12})}{sin (\frac{5 π}{12})}$ $A=25sin(pi/12)/sin((5pi)/12)$

$A=25((sqrt(6)-sqrt(2))/cancel4)/((sqrt(6)+sqrt(2))/cancel4)$

$A=25(sqrt(6)-sqrt(2))/(sqrt(6)+sqrt(2)$

$A=25(sqrt(6)-sqrt(2))/(sqrt(6)+sqrt(2))*(sqrt(6)-sqrt(2))/(sqrt(6)-sqrt(2)$

$A=25((6+2-2sqrt(12)))/(6-2)$

$A=25/4(8-4sqrt(3))$

$A=25(2-sqrt(3))$

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/125π12(5pi)/12. If side C has a length of 25 2525 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?