A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2π2. If side C has a length of 28 28 and the angle between sides B and C is pi/12π12, what is the length of side A?

1 Answer
Aug 11, 2018

A=7(sqrt6-sqrt2)~~7(1.0353)=7.2471A=7(62)7(1.0353)=7.2471.

Explanation:

Let us denote by /_(B,C)(B,C) the angle between sides B and CBandC.

Using the Sine-Rule, then, we have,

A/(sin/_(B,C))=B/(sin(/_C,A))=C/(sin(/_A,B))Asin(B,C)=Bsin(C,A)=Csin(A,B).

:. A/(sin/_(B,C))=C/(sin(/_A,B)).

:. A/sin(pi/12)=28/sin(pi/2)=28/1.

:. A=28sin(pi/12)=28{(sqrt3-1)/(2sqrt2)}.

rArr A=7(sqrt6-sqrt2)~~7(1.0353)=7.2471.