Right Angle Triangle Practice

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📚 Part 1: Achieved Level - Basic Pythagorean Theorem

1. Which of the following is a Pythagorean triad?

3, 4, 5

2, 3, 4

1, 2, 3

4, 5, 6

2. In a right angle triangle, the longest side is called the ___________.

3. Calculate the hypotenuse of a right triangle with sides 6 cm and 8 cm.

4. Find the hypotenuse when the two shorter sides are 5 m and 12 m.

5. A right triangle has sides 9 cm and 12 cm. What is the length of the hypotenuse?

⭐ Part 2: Merit Level - Finding Missing Sides

6. A right triangle has a hypotenuse of 13 cm and one side of 5 cm. Find the length of the third side.

7. The hypotenuse of a right triangle is 25 m and one side is 15 m. Calculate the other side.

8. A ladder is leaning against a wall. The ladder is 10 m long and the bottom is 6 m from the wall. How high up the wall does the ladder reach?

🏆 Part 3: Excellence Level - Problem Solving

9. A rectangular field is 80 m long and 60 m wide. What is the length of the diagonal path across the field? Show all working and round your answer to the nearest metre.

10. Sarah walks 400 m north, then 300 m east. How far is she from her starting point? Explain your method and justify your answer.

11. A television screen measures 32 cm high and 45 cm wide. What is the diagonal measurement (screen size) to the nearest centimetre? Show how you would check if your answer is reasonable.

12. Two Pythagorean triads that are multiples of 3, 4, 5 are:

Explain how you can create infinite Pythagorean triads from any basic triad: