Pythagoras Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, represented as $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse. In trigonometry, besides the Pythagorean Theorem, there are essential ratios that relate the angles and sides of right triangles. The two primary terms associated with right triangles are adjacent and opposite sides relative to a given angle. These sides are used to define sine, cosine, and tangent, which are vital for solving various problems in trigonometry:

Pythagoras’ Theorem is a rule used only for right‑angled triangles

✨ What are a, b, and c?

• a and b are the two shorter sides of the right‑angled triangle.
  These are called the legs.

• c is the longest side, opposite the right angle.
  This side is called the hypotenuse.

A quick way to remember:

• Hypotenuse = longest side = c

• The other two sides = a and b

📘 Example

Imagine a right‑angled triangle where:

• Side a = 3 cm

• Side b = 4 cm

We want to find c, the hypotenuse.🧠 Step‑by‑step using Pythagoras’ Theorem

Pythagoras says:

🧠 Step‑by‑step using Pythagoras’ Theorem

Pythagoras says:

$a^2+b^2=c^2$

1. Square the two shorter sides

$a^2=3^2=9$

$b^2=4^2=16$

2. Add them

$a^2+b^2=9+16=25$

3. Square‑root the result to get c

$c=\sqrt{25}=5$

✅ Final Answer 5