Question

The law of cosines is used to find the value of m.

Answer 1

sin(28) = m/27
or
m = 27 x (sin(28))

That's the easy way to find it, but if they want you to use cos, that is really tricky. They give you everything that cos would show.

you could just show a^2 + b^2 = c^2

(18)^2 + b^2 = (27)^2
324 + b^2 = 729
b^2 = 405
b = square root of 405
b = 20.1246117975

Answer 2

`m\approx 14`

Explanation:

We have been given an image of a triangle. We are asked to find value of side m using law of cosines.

We know that law of cosines is
`c^2=a^2+b^2-2ab\cdot \text{cos}(C)`.

For our given triangle
`c=m`,
`a=27`,
`b=18` and
`C=28^(\circ)`.

Upon substituting our given values in above formula, we will get:

`m^2=27^2+18^2-2\cdot27\cdot18\cdot \text{cos}(28^(\circ))`

`m^2=729+324-972\cdot 0.882947592859`

`m^2=1053-858.225060258948`

`m^2=194.774939741052`

`m=√(194.774939741052)`

`m=13.956179267`

`m\approx 14`

Therefore, the value of m is 14 units.