A triangle has sides A, B, and C. The angle between sides A and B is $(3pi)/4$ . If side C has a length of $1$ and the angle between sides B and C is $pi/12$ , what is the length of side A?

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Answer 1 · 2016-05-02T14:08:14

$color(blue)(A~~0.3660" to 4 decimal places")$

Good practice to draw a diagram so that you can see what is going on.
Tony B

It looks as though things are changing! I always understood that capital letters stood for the vertices (angles) and lower case was for the sides.

Momentarily using the notation I am used to in that Capital letters represent vertices:

Using the sine rule $" " a/(sin(A))=b/(sin(B))=c/(sin(C))$
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Using your notation:

$" "C/(sin(3/4 pi))=A/(sin(pi/12))$

But $C=1$ giving:

$" "1/(sin(3/4 pi))=A/(sin(pi/12))$

Multiply both sides by $sin(pi/12)$

$" "(sin(pi/12))/(sin(3/4 pi))=A$

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Note that $1/12 pi = 1/12xx180 = 15^o$

Note that $3/4pi=3/4xx180=135^o$
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$color(blue)(A~~0.3660" to 4 decimal places")$

A triangle has sides A, B, and C. The angle between sides A and B is (3pi)/4(3pi)/4. If side C has a length of 1 1 and the angle between sides B and C is pi/12pi/12, what is the length of side A?