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Pythagoras Triangle Problem Solving
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Pythagoras Triangle Problem Solving
Use the rule relating the squares of the two shorter sides to the square of the longest side in a right-angled triangle. Show your working for calculation questions.
Choose the best answer
1.In a right-angled triangle, which side is opposite the right angle?
- The shortest side
- The hypotenuse
- The base
- The adjacent side
2.Which equation gives the relationship between the two shorter sides, a and b, and the longest side, c, of a right-angled triangle?
- a + b = c
- a² + b² = c²
- a × b = c
- a² + b = c²
3.A triangle has side lengths 5 cm, 12 cm and 13 cm. What can you conclude about it?
- It is right-angled
- It is equilateral
- It cannot form a triangle
- It is obtuse but not right-angled
Solve the problems
Find the missing length. Include your calculation and write the answer with the correct unit.
4.A right-angled triangle has shorter sides of 9 cm and 12 cm. Find the longest side.
5.A 13 m support cable runs from the ground to the top of a vertical pole. Its ground anchor is 5 m from the foot of the pole. How high up the pole does the cable reach?
6.A rectangular sports court is 150 m long and 80 m wide. Calculate the straight-line distance from one corner to the opposite corner.
7.A carpenter measures 8 m along one side of a corner and 15 m along the other. If the corner is exactly 90°, what length should the diagonal between those measurements be?
Fencing cost challenge
Show each step of your calculation. Give the final cost in Australian dollars.
8.A triangular paddock has two sides, 90 m and 120 m, that meet at a right angle. Fencing costs $32 per metre. Find the length of the third side, the paddock's perimeter, and the total fencing cost.
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