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Right Angle Triangle Calculations
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Right Angle Triangle Calculations
Use the Pythagorean theorem to solve each problem. Show your working for calculation questions. Give exact answers where possible.
Pythagorean Theorem
1.Which equation gives the relationship between the legs a and b and the hypotenuse c of a right-angled triangle?
- a + b = c
- a² + b² = c²
- a² + c² = b²
- a × b = c²
2.Select every set of three lengths that could be the sides of a right-angled triangle.
- 8, 15, 17
- 9, 12, 15
- 10, 11, 15
- 7, 24, 25
3.A right-angled triangle has legs measuring 9 cm and 12 cm. Calculate the hypotenuse.
4.A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the length of the other leg.
5.A ferry ramp is 10 m long. Its lower end is 6 m horizontally from the point directly beneath its upper end. How high is the upper end of the ramp?
Using Right-Angled Triangles
6.A rectangular deck is 9 m long and 12 m wide. What is the length of a straight line from one corner to the opposite corner?
7.During a ferry trip, Oliver walks 8 km east from the harbour while Nikau travels 15 km north. Assuming their routes are at right angles, how far apart are they in a straight line?
8.A right-angled triangle has a hypotenuse of 20 cm and one leg of 12 cm. Calculate the other leg.
9.A television screen has a diagonal of 65 inches and a width of 56 inches. Assuming the screen is rectangular, calculate its height.
10.A right-angled triangle has side lengths in the ratio 3:4:5. If its shortest side is 21 cm, calculate the other two sides and check that the Pythagorean theorem holds.
11.A triangle has a right angle, a hypotenuse of 17 cm, and one leg of 8 cm. Georgia says the other leg is 15 cm. Is she correct? Use the Pythagorean theorem to justify your answer.
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