WEBVTT

1
00:00:00.000 --> 00:00:07.639
Here is the problem: Solve the triangle with sides a equals 7, b equals 8, c equals 9.

2
00:00:08.089 --> 00:00:14.486
Side a is opposite angle A, b opposite B and c opposite C. This is the SSS case.

3
00:00:15.286 --> 00:00:17.771
Each angle from the law of cosines.

4
00:00:18.221 --> 00:00:19.510
Area and perimeter.

5
00:00:20.310 --> 00:00:48.720
So the answer is a equals 7, b equals 8, c equals 9; A equals 48.1896851°, B equals 58.41186449°, C equals 73.3984504°; area equals 26.83281573, perimeter equals 24.

6
00:00:49.170 --> 00:00:57.994
Three measurements including a side normally fix a triangle. Two sides with a non-included angle (SSA) can give zero, one or two triangles.

7
00:00:58.794 --> 00:01:15.710
Triangle 1: angles sum to 180°; a/sin A equals 9.391485505 equals c/sin C equals 9.391485505.