A triangle has sides A, B, and C. The angle between sides A and B is #pi/8#. If side C has a length of #16 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-03-25T16:27:09

#A = 10.8 (3s.f.)#

sine rule:

#A/sin a = B/sin b = C/sin c#

the uppercase letters are sides, while the lowercase letters are angles opposite the sides.

angle #a# is the angle between #B# and #C#, angle #b# is the angle between #A# and #C#, and angle #c# is the angle between #A# and #B#.

angle between #A# and #B# = #pi/8#
angle between #B# and #C# = #pi/12#

#c = pi/8#
#a = pi/12#

#C = 16#

using the sine rule, #A/sin (pi/12) = 16/sin (pi/8)#

multiply by #sin (pi/12)#:

#A = (16sin(pi/12))/sin(pi/8)#

using a calculator with the radians (Rad) setting:

#A = 10.8 (3s.f.)#