Shapes EXERCISES
Pythagoras' theorem
1. You will need a calculator for this question and the other questions in this exercise. What is the length of the hypotenuse of the triangle below (to 1 decimal place)?
2. The two sides of the roof shown in this picture meet at a right angle. A builder needs to replace the horizontal beam that connects them (shown in red on the diagram). How long does the beam need to be (to 1 decimal place)?
3. What is the length of the side of the triangle that is labelled "? cm" on the diagram?
4. Lizzie rides her horse west for an unknown distance, then rides 2 km north. She ends up 5 km from the starting location. How far west did she ride (to 1 decimal place)?
5. What is the length of the side of the triangle that is labelled "? m" on the diagram?
6. Bobby wants to cycle from his house to the library. He can take the top road for 3 miles then turn right and cycle 2 miles, as shown on the map. How long is the direct route from Bobby's house to the library?
7. Which of the triangles shown below is a right-angled triangle?
8. Which of the triangles shown below is a right-angled triangle?
9. A ladder is leaning against a wall so that it reaches the top. The wall forms a right angle with the ground. The ladder is 3 m long and is 2 m away from the base of the wall. How tall is the wall (to 1 decimal place)?
10. A football pitch is 105 m x 68 m. If a footballer runs the diagonal length (as shown by the red dotted line on the diagram), how far does she run to the nearest metre?
Advertisement