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 #6 # and the angle between sides B and C is #pi/12#, what is the length of side A?

1 Answer
Nov 25, 2017

#A=(6sin(pi/12))/sin(pi/8)~=4.06#

Explanation:

We can use the the Law of sines, which states that the ratio of the length of a side to the sine of its opposite angle is equal for all sides and angles in a triangle. You can also express this using the following equation:

#sin(alpha)/a=sin(beta)/b=sin(gamma)/c#

where #alpha# is the opposite side to #a#, #beta# is the opposite side to #b# and #gamma# is the opposite side to #c#.

If you draw up the triangle, you can see that #pi/8# is the angle opposite #C# and #pi/12# is the angle opposite #A#. Using the Law of sines, we can setup the following equation:

#sin(pi/8)/6=sin(pi/12)/A#

#Asin(pi/8)=6sin(pi/12)# (using cross-multiplication)

#A=(6sin(pi/12))/sin(pi/8)~=4.06#