Question

A triangle has sides A, B, and C. Sides A and B are of lengths `6` and `8`, respectively, and the angle between A and B is `pi/4`. What is the length of side C?

Answer 1

`c=5.67` rounded to hundredth.

Explanation:

Cosine Law

`c^2 = a^2 + b^2 - 2abcos(theta)`

In our problem `a = 6` and `b=8` and we are also given the angle between as `pi/4`

To find `c` we plug in the values in the cosine law and we get.

`c^2 = 6^2 + 8^2 - 2*6*8*cos(pi/4)`
`c^2 = 36 + 64 - 96 (sqrt(2)/2)`
`c^2 = 100 - 48*sqrt(2)`
`c^2 = 32.117749006091437657518941237934` using calculator
`c = sqrt(32.117749006091437657518941237934)`
`c = 5.6672523330174242081448041317437`

`c=5.67` rounded to hundredth.