WEBVTT

1
00:00:00.000 --> 00:00:06.455
Here is the problem: Find all three angles of a triangle with sides 7, 8 and 13.

2
00:00:06.905 --> 00:00:09.749
SSS: find all three angles.

3
00:00:10.549 --> 00:00:18.386
Check the triangle inequality. 7 plus 8 equals 15 greater than 13, so a triangle exists.

4
00:00:18.836 --> 00:00:20.786
Angle C (opposite side c).

5
00:00:21.237 --> 00:00:22.746
Angle A (opposite side a).

6
00:00:23.196 --> 00:00:25.019
Third angle from the angle sum.

7
00:00:25.819 --> 00:00:28.814
Area from two sides and the included angle.

8
00:00:29.614 --> 00:00:42.780
So the answer is A approximately 27.795772°, B approximately 32.204228°, C approximately 120°.

9
00:00:43.230 --> 00:01:12.464
The triangle has sides a equals 7, b equals 8, c equals 13 and angles A approximately 27.795772°, B approximately 32.204228°, C approximately 120°. It is an obtuse scalene triangle with area approximately 24.248711 and perimeter approximately 28.

10
00:01:13.264 --> 00:01:17.200
A plus B plus C equals 180°.

11
00:01:17.650 --> 00:01:24.082
Heron prime s formula gives the same area: 24.248711.

12
00:01:24.532 --> 00:01:43.108
Law of sines ratios: a/sin A approximately 15.011107, b/sin B approximately 15.011107, c/sin C approximately 15.011107.