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

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Answer 1 · 2016-07-02T14:26:21

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

you know, by the Euler theorem, that

#A:sin hat(BC)=C:sin hat(AB)#

so, in this case:

#A:sin(pi/12)=25:sin((5pi)/12)#

by which you have:

#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))#