Summary Applications of Pythagoras theorem

Understanding When to Apply Pythagoras' Theorem to Right Angle Triangles

Identifying and Labeling Sides for Pythagoras' Theorem

 In a right angle triangle, the sides are labeled as follows:

 a and b: the two shorter sides

 c: the longest side, also known as the hypotenuse

 Pythagoras' theorem can only be applied if the triangle is a right angle triangle.

Applying the Pythagoras' Theorem Equation

 The Pythagorean theorem states that in a right angle triangle: a^2 + b^2 = c^2

 Where a and b are the lengths of the two shorter sides, and c is the length of the longest
side (hypotenuse)

Solving for Missing Lengths Using Pythagoras' Theorem

 To find a missing length using Pythagoras' theorem:

 If you are given the lengths of a and b: c = sqrt(a^2 + b^2)

 If you are given the lengths of a and c: b = sqrt(c^2 - a^2)

 If you are given the lengths of b and c: a = sqrt(c^2 - b^2)

Using Calculators to Simplify and Solve Pythagoras' Theorem Equations

 Use a calculator to find the square root of a number when solving for a missing length using
Pythagoras' theorem

Interpreting Corner Labels and Side Notation in Exam Questions

 Be familiar with the following corner labels and side notation in exam questions:

 Corner labels: A, B, C (right angle is always at C)

 Side notation: Opposite, Adjacent, Hypotenuse

Practical Applications of Pythagoras' Theorem to Real-World Problems

Pythagoras' theorem can be used to find missing distances or heights in real-world problems
involving right angle triangles, such as:

Measuring the height of a tall object, such as a tree or building

Finding the distance between two points in 2D space

Engineering and design applications, such as determining the length of a ramp or the size of a
support beam.