A triangle has sides A, B, and C. The angle between sides A and B is #(5pi)/6#. If side C has a length of #5 # and the angle between sides B and C is #pi/12#, what are the lengths of sides A and B?
1 Answer
Explanation:
Given two angles, the third one in a triangle is fixed. In this case it is
We now have three angles and a side, and can calculate the other sides using the Law of Sines.
The Law of Sines (or Sine Rule) is very useful for solving triangles:
Where: a, b and c are sides.
And it says that: When we divide side a by the sine of angle
it is equal to side b divided by the sine of angle
and also equal to side c divided by the sine of angle
https://www.mathsisfun.com/algebra/trig-sine-law.html
For the given problem values: