Pythagoras Theorem

Pythagoras 1

100

In the below equation what is the value of side a?

5² + 8² =89

5

200

solve for b (2 d.p)

a = 2.5

c = 5

4.33

300

List 2 ways that you can identify the hypotenuse of a triangle.

1. Opposite the right angle

2. Longest side

400

Sarah has a rectangular field that is 7 meters long and 4 meters wide. She wants to know the shortest distance from one corner to the opposite corner of the field. What is this distance?

28

500

Alex has a triangular sail for his toy boat. He knows the hypotenuse is 10 inches, and one of the other sides is 8 inches. What is the length of the third side?

6 inches

Pythagoras 2

100

solve for c² (2 d.p)

side a = 0.5

side b = 1.25

1.35

200

solve for a (2 d.p)

b = 4

c = 4

3

300

Explain how Pythagoras theorem works?

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.

400

Tim wants to put a diagonal wooden beam across the back of his bookshelf. If the bookshelf is 2m tall and 1.5m wide, how long does the wooden beam need to be?

2.5m

500

Alex is painting the wall of his room. He needs to reach the top corner, which is 10 feet above the floor. He stands 6 feet away from the wall. Can he use a 8-foot ladder, or does he need a longer one?  

No he can't, he will need a longer ladder.

Pythagoras 3

100

In the below equation what is the value of side b?

10² + 15² = C²

15

200

solve for b (2 d.p)

a = 9

c = 23

21.17

300

Can Pythagoras theorem be applied to any triangle?

- explain your answer.

No - it is only proven to work in right angled triangles.

400

Mia is drawing a path to connect the two ends of her garden. One side is 6 steps long, and the other side is 8 steps long. How many steps long will her path be if she makes it go directly across the garden?

10 steps

500

Liam is arranging his books on a shelf. He has two stacks of books, one with a height of 9 inches and the other with a height of 12 inches. If the stacks are positioned at a right angle, what is the shortest distance between the tops of the two stacks?

15 inches

Pythagoras 4

100

solve for c² (2 d.p)

a = 22

b = 33

39.66

200

solve for b (2 d.p)

c = 75

a = 48

57.63

300

What is the formula to calculate the hypotenuse?

a² + b² = c²  

400

Sarah is building a ramp for her toy car. The ramp needs to reach a height of 3 feet, and the base of the ramp is 4 feet away from the starting point. How long does the ramp need to be?

5 feet

500

Mia wants to make a rectangular garden bed. She knows one side is 5m, and the diagonal is 13m. What is the length of the other side?

12m

Pythagoras 5

100

Solve for C² (2 d.p) 

side a = 8

side b = 1.5

8.14

200

solve for a (2 d.p)

c = 98

b = 87

45.11

300

What are the 2 Pythagorean formulas used to calculate the shorter sides of a right-angle triangle?

a² = c² - b²

b² =c² - a²

400

Lisa is flying her kite. The kite string is 50 meters long, and the kite forms a right angle with the ground. If the kite's height above the ground is 30 meters, how far horizontally is Lisa from the point directly below the kite?

40m

500

Sarah is building a ramp for her pet turtle. If the ramp's base is 9 cm and the hypotenuse is 15cm, what is the length of the ramp?

12cm