Question

How do you use the law of cosines or law of sines if you are given a=55, b=25, c=72?

Answer 1

The Law of Cosines allows us to determine an angle given three sides.

Explanation:

The Law of Cosines:
`color(white)("XXXX")` `c^2 = a^2+b^2 -2abcos(C)`
or (rearranging)
`color(white)("XXXX")` `cos(C) = ((a^2+b^2)-c^2)/(2ab)`

`rArr` `color(white)("XXXX")` `C = arccos(((a^2+b^2)-c^2)/(2ab))`

plugging in the values:
`color(white)("XXXX")` `a=55`
`color(white)("XXXX")` `b=25`
`color(white)("XXXX")` `c=72`

`rArr` `color(white)("XXXX")` `C= arccos(((55^2+25^2)-72^2)/(2*55*25))`

`color(white)("XXXX")` `C = 2.16255` radians, or `123.905^@`

Similarly, we can calculate
`color(white)("XXXX")` `A = 0.6867` radians, or `39.346^@`
and
`color(white)("XXXX")` `B = 2.16255` radians, or `123.905^@`