What is Pythagoras? The Pythagoras rule has been attributed to the Greek mathematician Pythagoras and is a rule which connects the lengths of the sides of any Right angled triangle. Copy the formula into your book The Pythagoras rule: Why do we need to learn Pythagoras? There are many professions that use it everyday: mathematical experts, engineers, architects, surveyors, cartographers, carpenters, construction and building inspectors, electricians, glaziers, electrical installers, machinists, and managers in the construction and business industries.

In geometric form, Pythagoras rule states that: In any right angled triangle, the square on the hypotenuse is equal in area to the sum of the areas of the squares on the other two sides. Look through the Pythagorean Theorum powerpoint below:

Labeling the right angled triangle Labeling the triangle is extremely important so that you can use the formula correctly. The letter ‘c’ must always be on the longest side, which is always opposite the right angle as shown above. The other two sides can be labeled either ‘a’ or ‘b’.

Labeling the right angled triangles continued… Label the following triangles. Draw them in your book so that you can use it for revision.

Finding the hypotenuse Use the Pythagoras formula to calculate the unknown side. c 2 = a 2 + b 2

Finding the hypotenuse continued… Find the length of the hypotenuse of the following right angled triangles. Leave the answer as a surd (square root) if needed.

Finding the hypotenuse continued… Now try to find the hypotenuse when the measurements are in decimals.

Finding the hypotenuse activity Draw the following square accurately and divide it into the sections as shown below: Cut out the 6 parts of the square and then rearrange the shapes so that they look like the following:

Finding the hypotenuse activity continued… Answer the following questions once you have rearranged the shapes: 1.What is the total area of the two squares, A and B, that have not been used? 2.What is the area of the square C inside the second square ? 3.Explain why: Area of A + Area of B = Area of C 4. Explain why the length of the hypotenuse of the triangle is 5cm.

Finding the length of the third side Use the Pythagoras formula to calculate the unknown side. c 2 = a 2 + b 2

Finding the third side continued… Find the length of the third side of the following right angled triangles. Leave the answer as a surd (square root) if needed.

Finding the third side activity The following picture shows how the squares are drawn on a right angled triangle. Your challenge is to copy and complete the following table. You may wish to draw the triangles to help you.

Finding the unknown side What happens when one of the numbers is in Square Root form?

Finding the unknown side continued….

Problem Solving

Problem Solving Continued….

How can we use Pythagoras to solve word problems? A boat travels 45 km east then 60 km north, how far is it from where it started? Step 1: Draw a diagram Step 2: Label the side Step 3: Use Pythagoras to solve problem Step 4: Answer the question

Solving word problems continued…… 1) A kite is flying on a string which is 10m, the kite is flying 6m of the ground, if the kite plummets straight down how far will the kite flyer have to walk to pick it up? 2) A totem pole is tied to the ground with ropes stuck in the ground with pegs, if the rope is 14m long and the pole is 9m long, how far will the pegs be from the base of the totem pole? 3) A lighthouse shines a light on a ship, the light beam is 6.5km long, the ship is 5km away from the base of the lighthouse, how tall is the lighthouse? 4) A helicopter floats 120m above a helipad, a dog is 85m from the helipad, if the dog could fly, how far would it have to fly to get to the helicopter? 5) A runner starts running west for 4.5km then changes direction and runs 3km south. How far will the runner have to run to get back to the start? If they take the most direct route.

What is Trigonometry?

How do we label the 3 sides?

Labeling the 3 sides

Labeling the 3 sides continued

Trigonometry Ratios

Trigonometry Ratios to find an unknown length

Trigonometry Ratios

Finding an unknown length

Finding the Angle