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

2 Answers
Júlio B.
Jan 5, 2016

The length of a is 4/3

Explanation:

We are able to solve it using logic:
Since pi/8 = 2 we'll multiply both sides by 8 resulting in pi = 16.

Then, another logic: pi = 16, so pi/12 = 16/12 = 4/3.

I won't say units, its implicit.

SagarStudy
Jan 5, 2016

a=1.3524 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, angle between side "b" and "c" /_ A and angle between side "c" and "a" by /_ B.

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

It is given that side c=2.

Using Law of Sines
(Sin/_A)/a=(sin/_C)/c

implies Sin(pi/12)/a=sin((pi)/8)/2

implies 0.2588/a=0.3827/2

implies 0.2588/a=0.19135

implies a=1.3524 units

Therefore, side a=1.3524 units

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