A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4# and the angle between sides B and C is #pi/6#. If side B has a length of 12, what is the area of the triangle?

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Answer 1 · 2016-05-07T10:49:26

area of triangle is #(1/2)#(base)(height) = #(1/2)*A*B#
= #(1/2)#(12) #((12/(sin60π))*sin30º)#

Working in degree, π = 180º,

The Angle between C and A is
#(180º -90º -30º)# = 60º

Hence using sine rule,

#A/sin(angle between B&C)# = #B/sin(angle between C&A)# =
#C/sin(angle betwen A&B)#

And given that #angle between AB # is a right angle,

you need to only find A where

#A/sin(angle between B&C)# =#B/sin(angle between C&A)#,

#A= (B/sin(angle between C&A))*sin(angle between B&C)#

= #(12/(sin60π))*sin30º#

Hence, area of triangle is #(1/2)#(base)(height) = #(1/2)*A*B#
= #(1/2)#(12) #((12/(sin60π))*sin30º)#