A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2#. If side C has a length of #4 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2018-02-23T15:32:33

#A=1.04"cm"#

We have a triangle that looks like this:

enter image source here

Here, side B is the base leg, side C is the hypotenuse and side A is the vertical leg.

We can say the angle opposite to side A is #/_a#, and the angle opposite to side C is #/_c#.

#sina/A=sinb/B=sinc/C#

Since Side B doesn't matter here, we can say:

#sina/A=sinc/C#

We need to solve for #A#. Simply rearrange:

#A=(Csina)/sinc#

Since #a=pi/12, C=4"cm"# and #c=pi/2#, we can input:

#A=(4*sin(pi/12))/sin(pi/2)#

#A=(4*0.259)/1#

#A=1.04"cm"#