The Pythagorean Theorem Calculators
Knowledge
What is the Pythagorean theorem?
Pythagorean Theorem (also called Pythagoras theorem) is basically used to find the length of an unknown side and the angle of a triangle. If we know the lengths of the two sides of a right triangle, we can find the length of the third side. And it only applies to right triangles.
Why the Pythagorean Theorem is important?
The Pythagorean theorem is named after Pythagoras, a Greek mathematician in the 600 BC. But nobody knows when Pythagorean theorem really originated. The Pythagorean theorem was known and applied by the Babylonians as far back as about 3000 BC. Therefore, Pythagorean theorem has a history of at least 5000 years. The importance of Pythagorean theorem lies in that it is the first theorem in history to link numbers with shapes, that is, it is the first theorem to link geometry with algebra. The Pythagorean theorem is not a boring formula in math textbooks. It plays an important role in our real life, such as engineering construction, astronomy and geography.
How to use the Pythagorean Theorem?
To solve the Pythagorean theorem problem, we use the Pythagorean theorem formula. There are basically three situations:
If "c" denotes the length of the hypotenuse and "a" and "b" denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation:
a2 + b2 = c2
If the lengths of both "a" and "b" are known, then "c" can be calculated as:
c = a2 + b2
If the length of the hypotenuse "c" and of one side ("a" or "b") are known, then the length of the other side can be calculated as:
a = c2 - b2 or b = c2 - a2
Example 1
Find the value of ? in the triangle shown below.
42 + 32 = ?2
16 + 9 = ?2
25 = ?2
25 = ?2
5 = ?2
Example 2
Find the value of ? in the triangle shown below.
92 - 82 = ?2
81 - 64 = ?2
17 = ?2
17 = ?2
Example 3
Does this triangle have a Right Angle?
Solution:
using the Pythagorean theorem formula,
a2 + b2 = 102 + 242 = c2 = 100 + 576 = 676
c2 = 676 = 262
Pretty easy huh? There are more challenging questions in Geometry Q&A.If you want to get a high score on the math test, be sure to check out these questions.
