Question

Use the Law of Cosines to find the missing angle. Find m∠A to the nearest tenth of a degree.

Answer 1

Firstly, we can look at our givens,

a = 17

b = 22

c = 30

And we are looking for m∠A

$a^2=b^2 +c^2 -2bc (cosA)$ Is the Law of Cosines. Now we can solve for our unknown, m∠A. This will give us

$A = cos^{-1} (\frac{-a^2+b^2+c^2}{2bc})$

Now we can substitute in our given variables.

$A= cos^{-1} (\frac{-(17^2)+27^2+30^2}{2(27)(30)} )$

Then we can plug this into our calculator which will give us

34.19185257 degrees

Now we just have to round to the nearest tenth

This means that the answer is 34.2 degrees

Answer 2

For this case we have:

In the attached image, we state the law of cosine at the beginning. Then, the angle that you want to find is identified. Once the angle is identified, the formula of the corresponding side is chosen.

The data is replaced and the required angle is cleared following the steps of the attached image.

Answer:

33.9 degrees

See attached image