Right Angle Triangle Calculations

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📐 Part 1: Pythagorean Theorem and Basic Calculations

1. Which of the following is the correct formula for the Pythagorean theorem? (Achieved)

a + b = c

a² + b² = c²

a² + c² = b²

a × b = c²

2. Which of these are Pythagorean triads? Select all that apply. (Achieved)

3, 4, 5

5, 12, 13

6, 8, 10

7, 24, 25

3. A right triangle has legs of 6 cm and 8 cm. Calculate the length of the hypotenuse. Show your working. (Achieved)

Answer: ________ cm

4. The hypotenuse of a right triangle is 10 cm and one leg is 6 cm. Find the length of the other leg. (Merit)

Answer: ________ cm

5. A ladder is leaning 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? (Merit)

Answer: ________ metres

📏 Part 2: Advanced Applications

6. A rectangular field is 80 metres long and 60 metres wide. What is the diagonal distance across the field? (Merit)

Answer: ________ metres

7. Two ships leave a harbour at the same time. Ship A travels 15 km north, and Ship B travels 20 km east. What is the straight-line distance between the two ships? (Merit)

Answer: ________ km

8. A right triangle has a hypotenuse of 25 cm. If one angle is 37°, and the adjacent side to this angle is 20 cm, verify this is correct using the Pythagorean theorem. (Excellence)

Is this triangle correct? ____________

Explain your reasoning: ________________________________

9. A television screen is advertised as 55 inches (measured diagonally). If the screen has a width of 48 inches, what is the height of the screen? (Excellence)

Answer: ________ inches

10. A right triangle has sides in the ratio 5:12:13. If the shortest side is 15 cm, find the lengths of the other two sides and verify your answer using the Pythagorean theorem. (Excellence)

Second side: ________ cm

Hypotenuse: ________ cm

Verification: ________________________________

Right Angle Triangle Calculations

Right Angle Triangle Calculations

📐 Part 1: Pythagorean Theorem and Basic Calculations

📏 Part 2: Advanced Applications

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