The Pythagoras theorem is mentioned in several areas of mathematics. It is a crucial subject, particularly in the chapters on trigonometry. Pythagoras’ theorem recognizes as the Pythagorean theorem. According to Pythagoras’ theorem, the sum total of the squares of the 2 sides of a right-angled triangle, that is the base and perpendicular, is directly proportional to the square of the triangle’s hypotenuse. The Pythagorean theorem notion makes it relatively simple to determine the various values of the trigonometric ratios in any given right triangle. In this post, we will go through the Pythagorean theorem as well as its application to the right-angled triangle in great depth.
Define Right Angle
When we think of right angles, we often visualize a triangle. This is a common geometric figure and a powerful tool for understanding the world around us. The angles of a triangle can think of as the distances from one corner to the opposite side and from the opposite side to the adjacent corner. The three angles of a right angle triangle are all equal and sum up to 180 degrees. The type of triangle that has a 90-degrees angle between its base and the height, we call the triangle a right-angled triangle.
Here, we notice that the triangle is a right triangle and has two sides equal, so the swing is a right-angled isosceles triangle.
What is Pythagoras Theorem?
This fundamental theorem was discovered on a 4,000-year-old Babylonian tablet. This tablet is now often referred to as the Plimpton 322. This theory, though, was not widely accepted until Pythagoras entered the scene. Pythagoras was indeed a Greek philosopher who flourished in the sixth century BC. He was a philosopher & mathematician who promoted this theory in Italy, Egypt, as well as Babylon.
Let’s discuss the Pythagoras theorem formula as well the concept of the Pythagoras Theorem.
Pythagoras Theorem Equation & Formula
The Pythagorean theorem equation is critical since it will be utilized in many other sections throughout the course. You will be unable to answer a variety of difficulties until you comprehend this equation. The Pythagorean theorem formula is: a.a equals b.b + c.c, where c denotes the base of the given triangle, b denotes the perpendicular also known as the height of the given right-angled triangle, and c is its hypotenuse.
Let us provide an instance to better comprehend the Pythagoras theorem formula.
Example 1) The given hypotenuse of a right-angled triangle is 5 units long, while one of the triangle’s sides is 4 units long. Determine the length of the triangle’s left side.
Solution) We already know the formula to calculate the length of the third side using the Pythagoras theorem. The formula equals a.a = b.b + c.c
Let’s note down the information given to us in the question, the hypotenuse (a) in the equation is 5 cm which is the longest side of the triangle, the other given side of the triangle measures 4 units which is either the base or the height.
We will assume that the length of the third side is equal to y units.
Using the formula and putting the values in the Pythagoras formula we get,
5*5 = 4*4 + y*y which is equal to 25 = 16+ y*y
Now, solving the equation 25-16 = y*y, we get the value as 9 = y*y
Since y*y = 9, the value of y is equal to 3
Therefore, the measure of the remaining side of the triangle is equal to 3 units.
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