Question

A triangle has sides A, B, and C. Sides A and B are of lengths `2` and `4`, respectively, and the angle between A and B is `(7pi)/8`. What is the length of side C?

Answer 1

c=5.8737

Explanation:

The figure explaining the given data is given below:

To find side 'c', Cosine rule would apply in this case. Cosine rule says that

Cos C= `(a^2+b^2-c^2)/(2ab)`. Plugging in the given values, it would be

`Cos ((7pi)/8) =(4+16-c^2)/16`

`c^2= 20-16cos( (7pi)/8)= 20- 16cos (pi-pi/8)= 20+16cos (pi/8)= 20+14.5009= 34.5009`

c=5.8737