Question

How do you solve a triangle if you are given a=2.5, b=10.2, c=9?

Answer 1

`/_A = 0.229406` radians
`/_B = 1.953156` radians
`/_C = 0.959031` radians

Explanation:

For a triangle with
`color(white)("XXXX")`side `a` opposite angle `A`
`color(white)("XXXX")`side `b` opposite angle `B`
`color(white)("XXXX")`side `c` opposite angle `C`
The Law of Cosines says:
`color(white)("XXXX")` `c^2 = a^2+b^2-2abcos(C)`
or
`color(white)("XXXX")` `cos(C) = (a^2+b^2-c^2)/(2ab)`
`color(white)("XXXX")` `color(white)("XXXX")`(and similarly for `A` and `B`)

So
`color(white)("XXXX")` `cos(C) = (2.5^2+10.2^2-9^2)/(2(2.5)(10.2))`

`color(white)("XXXX")` `color(white)("XXXX")` `=0.574314`

`C = "arccos"(cos(C))`
`color(white)("XXXX")` `C = "arccos"(0.574314)`
`color(white)("XXXX")` `color(white)("XXXX")` `=0.959031` radians
`color(white)("XXXX")` `color(white)("XXXX")`(using a calculator)

Similar calculations can be made for angles `A` and `B`