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Right Angle Triangle Practice

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Right Angle Triangle Practice

Use the Pythagorean theorem for right-angled triangles: a² + b² = c², where c is the hypotenuse (the side opposite the right angle). Show your working and include units.

Warm-up: Spot the right triangle

1.A triangle has side lengths 3 cm, 4 cm and 5 cm. Which side is its hypotenuse, and how can you check that these lengths make a right-angled triangle?

2.Choose the set that could be the side lengths of a right-angled triangle: A) 2, 3, 4 B) 5, 12, 13 C) 4, 5, 6. Explain using the theorem.

A) 2, 3, 4
B) 5, 12, 13
C) 4, 5, 6

Build and solve

3.A triangular flag has perpendicular sides 6 cm and 8 cm. Find the length of the longest side.

4.A rectangular garden is 5 m wide and 12 m long. A straight stepping-stone path crosses from one corner to the opposite corner. How long is the path?

5.A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Find the other shorter side.

6.A 10 m ladder leans against a vertical wall. Its feet are 6 m from the wall. How high up the wall does it reach?

Solve the challenge

7.Mere walks 400 m north, then 300 m east. Assuming she walks in straight directions at right angles, how far is she from her starting point?

8.A rectangular sports court is 24 m long and 10 m wide. What is the length of its diagonal, to the nearest metre?

9.A right-angled triangle has shorter sides 9 cm and 12 cm. Find its hypotenuse, then state whether it is longer than 14 cm.

10.A builder uses a 3 m, 4 m, 5 m triangle to check a corner is square. If the two shorter sides are each doubled, what are the new three side lengths? Check that the new lengths still form a right-angled triangle.