WEBVTT

1
00:00:00.000 --> 00:00:08.290
Here is the problem: Two sides of a triangle are 6 and 9 with a 120° angle between them. Find the third side.

2
00:00:08.739 --> 00:00:12.605
SAS: find the third side and the remaining angles.

3
00:00:13.405 --> 00:00:19.953
Substitute into c squared equals a squared plus b squared minus 2ab times cos C.

4
00:00:20.403 --> 00:00:21.657
Take the square root.

5
00:00:22.107 --> 00:00:25.393
Find angle A with the law of cosines rearranged.

6
00:00:25.843 --> 00:00:29.454
Angles of a triangle add to 180°.

7
00:00:30.254 --> 00:00:33.064
Area from two sides and the included angle.

8
00:00:33.864 --> 00:00:53.195
So the answer is c equals 3the square root of 19 approximately 13.07669683; A approximately 23.413224°, B approximately 36.586776°.

9
00:00:53.645 --> 00:01:28.417
The triangle has sides a equals 6, b equals 9, c approximately 13.076697 and angles A approximately 23.413224°, B approximately 36.586776°, C approximately 120°. It is an obtuse scalene triangle with area approximately 23.382686 and perimeter approximately 28.076697.

10
00:01:29.217 --> 00:01:33.164
A plus B plus C equals 180°.

11
00:01:33.614 --> 00:01:40.127
Heron prime s formula gives the same area: 23.382686.

12
00:01:40.577 --> 00:02:00.511
Law of sines ratios: a/sin A approximately 15.099669, b/sin B approximately 15.099669, c/sin C approximately 15.099669.