Question

Use the law of cosines to solve for the length of side b. Show all of your work for full credit.

Answer 1

According to the law of cosines:

$AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot\cos33^{\circ}$.

Substituting all the values we know and finding $\cos33^{\circ}\approx0.84$ using a calculator, we have:

$b^2=16^2+11^2-2\cdot 16\cdot 11\cdot 0.84\\\\b^2=256+121-295.68\\\\b^2=81.32\\\\b=\pm \sqrt{81.32} \approx\pm9$


We discard the negative solution clearly.



Answer: b=9 units

Answer 2

The law of cosines states that: 
c² = a² + b² - 2ab*cos(C)
In this case, a and b are the legs we know the length of, and C is the degree opposite the unknown leg, or 33°
Plugging in:
c² = 11² + 16² - 2(11)(16)(cos(33°)
c² = 121 + 256 - 352 (.83)
c² = 81.78
c = 9

The length of side b is about 9