Tangent (tanθ): This one tells us the ratio of the “opposite” side to the “adjacent” side.Cosine (cosθ): This is another magic number that tells us the ratio of the “adjacent” side to the “hypotenuse.” It’s like finding out what part of the rectangular plot’s width is taken up by its diagonal.Sine (sinθ): This is like a magic number that tells us the ratio of the “opposite” side to the “hypotenuse.” It’s like finding out what part of the rectangular plot’s length is taken up by its diagonal.There are three main trigonometric ratios we use: Using Trigonometric Ratios: Now, let’s say we’re interested in finding the relationship between these sides.The Hypotenuse (Diagonal): The longest side, opposite the right angle, is called the “hypotenuse.” It’s like the diagonal of the rectangular plot.It’s like the length of the same rectangular plot of land. The Tall Side (Opposite): The side opposite to the right angle is taller, and we’ll call it the “opposite” side.It’s like the width of a rectangular plot of land. The Short Side (Adjacent): One side of the triangle is shorter, and we’ll call it the “adjacent” side.The Right-Angled Triangle: Imagine a triangle with one corner forming a perfect right angle, just like the corner of a piece of paper.Let’s explain this using a simple working model: Trigonometric ratios are a way of understanding the relationships between the sides of a right-angled triangle. It’s as if the squares on the shorter sides add up perfectly to the square on the longer side! That’s why it’s so useful in geometry and real-life situations where triangles are involved. So, in simple words, the Pythagorean Theorem is like a secret trick that helps us figure out the lengths of sides in a right-angled triangle. It says that in any right-angled triangle, the square of the length of the hypotenuse (the longest side, ‘C’) is equal to the sum of the squares of the other two sides (‘A’ and ‘B’). The Rule: This magical equality is the Pythagorean Theorem.The Interesting Discovery: Here’s the magic part! When you compare the area of the square on side ‘A’ plus the area of the square on side ‘B’, it’s exactly the same as the area of the square on side ‘C’!.For side ‘A’, make a square with ‘A’ on each side. The Squares: Now, we’re going to make squares on each of these sides.It’s like the diagonal of the rectangular plot. The Long Side (C): The third side, opposite the right angle, is longer and we’ll call it ‘C’.The Other Short Side (B): Another side is also short, and we’ll call it ‘B’.The Short Side (A): One side of the triangle is shorter, and we’ll call it ‘A’.The Right-Angled Triangle: Imagine a triangle with one corner forming a perfect right angle, like the corner of a piece of paper.Here’s how you can explain it in layman terms: A working model to demonstrate the Pythagorean Theorem could be a physical representation of a right-angled triangle along with squares on each side.
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