How do you use the law of cosines or law of sines if you are given a = 9, b = 12, c = 15 ?

1 Answer
Jim H
May 23, 2015

If you do not notice that it is a multiple of the 3-4-5 triangle, use the law of cosines to find an angle.

To use the law of sines: #sinA/a = sinB/b# , we need to knoe three of the 4 values. We would need and angle to use it.

For the law of cosines, it is simplest to find the larget angle first, so find angle C:

#c^2 = a^2+b^2-2abcosC#

#15^2 = 9^2+12^2-2(9)(12)cosC#

#225 = 81 + 144 - 216 cosC#

#225 = 225-216cosC#

#cosC =0#

The only angle between #0^@# and #180^@# with cosine equal to #0# is #C= 90^@#

Now, you have an angle and you can use the law of sines to find another angle.
Then again for the third, but knowing two angles, it's easier to find the third by addition/subtraction.

Although, now that we know it is a right triangle, we can use the definitions of the trigonometric functions to find the other angles.

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