"GCSE Maths Revision: Demystifying Pythagoras and Trigonometry with Practical Examples"

Understanding Pythagoras' Theorem

Pythagoras' Theorem is a fundamental principle in geometry that relates the lengths of the sides of a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Formula

The formula is expressed as:

a² + b² = c²

Where c is the hypotenuse, and a and b are the other two sides.

Practical Example

Consider a triangle with sides of 3 cm and 4 cm. To find the hypotenuse:

• Calculate: 3² + 4² = 9 + 16 = 25
• Find the square root of 25, which is 5 cm.

Introduction to Trigonometry

Trigonometry deals with the relationships between the angles and sides of triangles. It is especially useful in calculating unknown lengths or angles in right-angled triangles.

Basic Trigonometric Ratios

• Sine (sin): Opposite side over Hypotenuse
• Cosine (cos): Adjacent side over Hypotenuse
• Tangent (tan): Opposite side over Adjacent side

Practical Example

To find the angle in a triangle where the opposite side is 5 cm and the hypotenuse is 10 cm:

• Use the sine ratio: sin(θ) = 5/10 = 0.5
• Find θ using a calculator: θ = sin^-1(0.5) = 30°

By mastering these concepts, students can solve a variety of geometric problems and gain a deeper understanding of mathematical relationships.