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

Answer:

$m\approx 14$  

Step-by-step 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:

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

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

$m^2=1053-858.225060258948$  

$m^2=194.774939741052$  

$m=\sqrt{194.774939741052}$

$m=13.956179267$  

$m\approx 14$  

Therefore, the value of m is 14 units.