A triangle has sides A, B, and C. The angle between sides A and B is (7pi)/127π12. If side C has a length of 16 16 and the angle between sides B and C is pi/12π12, what is the length of side A?

1 Answer
SagarStudy · Júlio B.
Jan 5, 2016

a=4.28699a=4.28699 units

Explanation:

First of all let me denote the sides with small letters a, b and c
Let me name the angle between side "a" and "b" by /_ C∠C, angle between side "b" and "c" /_ A∠A and angle between side "c" and "a" by /_ B∠B.

Note:- the sign /_∠ is read as "angle".
We are given with /_C∠C and /_A∠A.

It is given that side c=16.c=16.

Using Law of Sines
(Sin/_A)/a=(sin/_C)/csin∠Aa=sin∠Cc

implies Sin(pi/12)/a=sin((7pi)/12)/16⇒sin(π12)a=sin(7π12)16

implies 0.2588/a=0.9659/16⇒0.2588a=0.965916

implies 0.2588/a=0.06036875⇒0.2588a=0.06036875

implies a=0.2588/0.06036875=4.28699 implies a=4.28699 ⇒a=0.25880.06036875=4.28699⇒a=4.28699 units

Therefore, side a=4.28699a=4.28699 units

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