Pythagoras Theorem is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. It is also sometimes called the Pythagorean Theorem. The formula and proof of this theorem are explained here with examples in the video below. This theorem is basically used for the right-angled triangle and by which we can derive base, perpendicular and hypotenuse formula. The theorem is named after a greek Mathematician called Pythagoras.
Pythagoras Theorem Statement
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
FUN FACT:
2.SINE, COSINE, TANGENT (SOHCAHTOA)
Sine, cosine, and tangent are the three main functions in trigonometry. They're all based on ratios obtained from a right triangle. Before we can discuss what ratios work for which function, we need to label a right triangle.
Opposite is the side opposite the angle in question, adjacent is the side next to the angle in question, and the hypotenuse is the longest side of a right triangle. The hypotenuse is always opposite the right angle.
The ratios that allow you to determine the sine, cosine, and tangent of a right triangle are:
• The sine of an angle is equal to the side opposite the angle divided by the hypotenuse.
• The cosine of an angle is equal to the side adjacent to the angle divided by the hypotenuse.
• The tangent of an angle is equal to the side opposite the angle divided by the side adjacent to the angle.
SOHCAHTOA
These ratios can be difficult to remember. You might easily get confused and not remember which side goes where. SOHCAHTOA is a mnemonic device helpful for remembering what ratio goes with which function.
• SOH = Sine is Opposite over Hypotenuse
• CAH = Cosine is Adjacent over Hypotenuse
• TOA = Tangent is Opposite over Adjacent
With these properties, you can solve almost any problem related to finding either a side length or angle measure of a right triangle. SohCahToa can ensure that you won't get them wrong.
3.ANGLES(30, 45, 60, 90)
ANGLES 30, 45, 60, 90 ARE CALLED SPECIAL ANGLES. THE VIDEO BELOW briefly gives an explanation.
4.THE SINE RULE
The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known.
Finding Sides
If you need to find the length of a side, you need to use the version of the Sine Rule where the lengths are on the top:
a/sin(A) = b/sin(B)
You will only ever need two parts of the Sine Rule formula, not all three.
You will need to know at least one pair of a side with its opposite angle to use the Sine Rule.
5.THE COSINE RULE
The Cosine Rule can be used in any triangle where you are trying to relate all three sides to one angle.
Finding Sides
If you need to find the length of a side, you need to know the other two sides and the opposite angle.
You need to use the version of the Cosine Rule where a2 is the subject of the formula:
a2 = b2 + c2 – 2bc cos(A)
Side a is the one you are trying to find. Sides b and c are the other two sides, and angle A is the angle opposite side a.