Right Angle Triangles & The Pythagorean Theorem
Hi there. This post is about right angle triangles and the Pythagorean Theorem.
Right Angle Triangles
A triangle is an enclosed two dimensional shape which has three sides, three corners and three angles. The three angles inside a triangle is equal to 180 degrees.
If one of the three angles in a triangle is 90 degrees (with the other two angles being less than 90 degrees), the triangle is a right angled triangle.
The Pythagorean Theorem For Finding Side Lengths
If you know two of the three side lengths of a right angled triangle, you can use the Pythagorean Theorem to find the third side length. The key formula is:
where the side lengths a and b are the legs of the triangle and the longest side length c is called the hypotenuse.
The formula above refers to the squares made from each of the side lengths. The square with the hypotenuse length is equal to the two squares with the side length aand side length b.
The hypotenuse of a right angle triangle is always opposite to the right angle.
Examples
Example One
The legs of a right angled triangle have side lengths of 1 and 3. What is the length of the hypotenuse?
The positive square root is used as distances have to be non-negative.
Example Two
From this image below, the missing side is the hypotenuse.
Example Three
The known side lengths of a right angle triangle are 3 units for the hypotenuse and 2 units for one of the two legs. What is the length of the second leg?
Let c be the length of the hypotenuse, let b the length of the second leg and let a be the length of the first leg of the right angled triangle.
The length of the second leg is about 2.236 units.
Some Special Cases: Pythagorean Triples
The Pythagorean formula consists of three numbers including the length of the hypotenuse. Pythagorean triples are three numbers which satisfy the equation:
Some Pythagorean triples (a, b, c order) include:
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
You can also have multiples of the Pythagorean triples such as 6, 8 and 10 which is two times the 3, 4, 5 triple.