A triangle has sides A, B, and C. The angle between sides A and B is #pi/6#. If side C has a length of #6 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-10-23T16:12:08

#color(magenta)(3.106 units#

#:.cancelpi^color(magenta)1/cancel6^color(magenta)1xxcancel180^color(magenta)30/cancelpi^color(magenta)1=30^@#

#:.cancelcolor(magenta)pi/cancel12^color(magenta)1xxcancel180^color(magenta)15/cancelcolor(magenta)pi=15^@#

#:.A/(sin15^@)=6/(sin30^@)#

#:.A=(6xxsin15^2)/sin30^@#

#:.A=(6xx0.258819045)/0.5#

#:.A=1.552914271/.5#

#:.color(magenta)(A=3.106# units to the nearest 3decimal places