Question

A triangle has sides A, B, and C. Sides A and B are of lengths `2` and `1`, respectively, and the angle between A and B is `pi/3`. What is the length of side C?

Answer 1

`C = sqrt3` or `~~1.73`

Explanation:

When you have the lengths of two sides of a triangle and the angle between, then you can solve the missing side with the law of cosines.

We want side `C`, which can be solved by the Law of Cosines formula `C = sqrt(A^2 + B^2 - 2(A)(B)cosc`, where `cosc` is the angle opposite to side `C`.

Let's substitute in the values and solve:
`C = sqrt((2)^2 + (1)^2 - 2(2)(1)cos(pi/3)`

Now simplify:
`C = sqrt(4 + 1 - 4(1/2)`

`C = sqrt(5 - 2)`

`C = sqrt3`

You can leave it like that, but if you want the answer to be in decimal form, it is `~~1.73` (rounded to the nearest hundredth's place).

Hope this helps!