How do I go about finding the remaining angles and sides

Question

1a. b=30, c=60, Angle A=70degrees

2a. a=20, b=25, c=22

I am sure I am meant to use the law of cosines, but for the first one, I keep getting values that seem too small. like less than 1. Is there something I am doing wrong? The second one seems a lot more straightforward

Answer 1

Once you have have two angles, the third can be found by subtracting their sum from 180 degrees. This can also be used as a check if you have found all three angles by other means (law of cosines and or law of sines).

NOTE that the law of sines does not work all the time. It may provide zero, one, or two results.

Always check to make sure your calculator is in the correct mode. For these triangle problems, you should select degree mode, not radian mode before starting to enter a problem.

There are two versions of the law of cosines. One finds you the angle between two known sides, and the other finds you the side across from a given (or known) angle and two given (or known) surrounding sides.

You can use this version of the law of cosines to solve the second problem.

Once you have the cosine of an angle, you can apply the cos^-1 (cosine inverse) function on your calculator to determine the angle.

As a check, here are the answers to the second problem. Make sure you can do this type of problem, or you will do poorly when test time arrives. Your teacher will also want to see your work, so use the above formulas with the given values for this problem.

Angles:

A = 49.8684 °

B = 72.8833 °

C = 57.2483 °

Answer 2

a² = b² + c² - 2bccosA

a² = 30² + 60² - 2(30)(60)cos70°

a² = 4500 - 1231.272516

a² = 3268.727 So a = 57.2

Use the Law of Sines to find angle C, then find angle B.