A triangle has sides A, B, and C. The angle between sides A and B is pi/4. If side C has a length of 5 and the angle between sides B and C is pi/12, what is the length of side A?

1 Answer
Yonas Yohannes
Jan 19, 2016

A = C sina/sinc;

substitute the values
A = 5 sin15/sin60
and A = 5((2sqrt2 +sqrt3)/3)
Plug in your calculator if you like
Hope it helps

Explanation:

Using the triangle angle theorem
we find the third angle is 120 thus

180 = anglea+angleb+anglec
Thus,
anglea = 15; angleb=45 and anglec = 120
Now you can use sin law to to compute side A
A/sina = B/sinb =C/sinc
Use the the 1st and third identities with respect to a, A, c, C
A = C sina/sinc; substitute A = 5 sin15/sin120= 5 sin15/sin60=
It uses the fact that sin60 = sin120 and
and
sin60 = (sqrt3)/2
sin15= ((sqrt3)+1)/((sqrt2)/2) sothen

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