WEBVTT

1
00:00:00.000 --> 00:00:06.571
Here is the problem: A right triangle has hypotenuse 13 and one leg 5. Find the other leg.

2
00:00:07.021 --> 00:00:11.851
Find the missing leg of a right triangle from the other leg and the hypotenuse.

3
00:00:12.651 --> 00:00:15.704
Rearrange the Pythagorean theorem for a leg.

4
00:00:16.154 --> 00:00:18.058
Substitute and simplify.

5
00:00:18.508 --> 00:00:20.342
Take the positive square root.

6
00:00:20.792 --> 00:00:22.081
Area and perimeter.

7
00:00:22.881 --> 00:00:30.602
Acute angles. Angle A is opposite leg a and angle B is opposite leg b; the right angle C is 90°.

8
00:00:31.402 --> 00:00:47.853
So the answer is b equals 12; area equals 30; perimeter approximately 30; angles approximately 22.619865°, 67.380135°, 90°.

9
00:00:48.303 --> 00:00:59.913
In every right triangle the square on the hypotenuse equals the sum of the squares on the two legs. Knowing any two sides fixes the third, and the angles follow from the tangent ratio.

10
00:01:00.713 --> 00:01:08.747
Check: a squared plus b squared equals 169 and c squared equals 169, which agree.

11
00:01:09.197 --> 00:01:14.619
(5, 12, 13) is a Pythagorean triple: all three sides are whole numbers.

12
00:01:15.069 --> 00:01:27.643
Angle sum: 90° plus 22.619865° plus 67.380135° equals 180°.