Question

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?

Answer 1

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

Explanation:

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

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")`