Question

Select the angle that correctly completes the law of cosines for this angle

Answer 1

A

Explanation:

Correct answer is A

Answer 2

Answer: Option A.

Explanation:

1. By definition the law of cosine is:

`c^(2)=a^(2)+b^(2)-2ab cos(C)`

2. By definition, the angle
`C` is opposite to the side whose length is
`c`.

3. Then, as you can see in the figure attached in the problem the length of the side c is:

`c=12`

3. Therefore, you can conclude that the measure of the angle
`C` is 67°.

4. To verify you can solve for the angle, as following:

`12^(2)=5^(2)+13^(2)-2(5)(13)cos(C)\\\\-12^(2)+5^(2)+13^(2)= 2(5)(13)cos(C)\\\\(-12^(2)+5^(2)+13^(2))/(2(5)(13)) = cos(C)\\\\arcos((-12^(2)+5^(2)+13^(2))/(2(5)(13))) = C\\C=67\°`

Then, the answer is the option A.