Right Angle Triangle Calculations

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Date:

📐 Part 1: Pythagorean Theorem and Basic Calculations

1. Achieved Level: Which of the following is a Pythagorean triad?

2, 3, 4

3, 4, 5

4, 5, 6

5, 6, 7

2. Achieved Level: In a right angle triangle, if the two shorter sides are 6 cm and 8 cm, what is the length of the hypotenuse?

Answer: ________ cm

3. Achieved Level: A right angle triangle has a hypotenuse of 13 cm and one side of 5 cm. Calculate the length of the third side.

Answer: ________ cm

4. Merit Level: A ladder is placed against a wall. The ladder is 5 metres long and the base of the ladder is 3 metres from the wall. How high up the wall does the ladder reach?

Height: ________ metres

🎯 Part 2: Problem Solving and Applications

5. Merit Level: A rectangular television screen has a width of 48 cm and a height of 36 cm. What is the diagonal measurement of the screen?

Diagonal: ________ cm

6. Merit Level: Sarah walks 12 km north, then 9 km east. How far is she from her starting point in a straight line?

Distance: ________ km

7. Excellence Level: A right angle triangle has sides in the ratio 5:12:13. If the perimeter of the triangle is 60 cm, find the actual lengths of all three sides.

Shortest side: ________ cm

Middle side: ________ cm

Hypotenuse: ________ cm

8. Excellence Level: A square has a diagonal of 10√2 cm. Calculate the area of the square.

Area: ________ cm²

🔍 Part 3: Advanced Applications

9. Excellence Level: A cone has a height of 8 cm and a base radius of 6 cm. Calculate the slant height of the cone.

Slant height: ________ cm

10. Excellence Level: Two ships leave a port at the same time. One travels north at 15 km/h and the other travels east at 20 km/h. How far apart are they after 2 hours?

Distance apart: ________ km

11. Challenge: Prove that the triangle with sides 7, 24, and 25 is a right angle triangle. Show your working clearly.

12. Reflection: Explain in your own words when you would use the Pythagorean theorem in real life. Give two examples.