The Pythagorean theorem is a very important theorem in geometry that describes the relationship between the three sides of a right triangle. The formula for the Pythagorean theorem is as follows:
In a right triangle, the sum of the squares of the two right sides is equal to the square of the hypotenuse of the right triangle.
In mathematical notation, it is: a + b = c
where A and B are the two right-angled sides of a right-angled triangle, and C is the hypotenuse.
A direct application of the Pythagorean theorem can be used to calculate the third edge from the two sides of a right triangle.
Here are some examples of using the Pythagorean theorem:
1.It is known that the two right-angled sides of a right-angled triangle are 3 and 4 respectively, find the length of the hypotenuse.
According to the Pythagorean theorem, we can substitute known values into the formula:
3² +4² = c²
9 + 16 = c²
25 = c²
c = √25
c = 5 So, the hypotenuse length of this right triangle is 5.
2.Knowing that the hypotenuse of a right triangle is 10 and the length of one right angle is 6, find the length of the other right angle.
In the same way, we can substitute a known value into the formula:
6² +c² = 10²
36 + c² = 100
c² = 64
c = √64
c = 8 So, the length of the other right-angled side of this right-angled triangle is 8.