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Right Angle Triangle Calculations
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Right Angle Triangle Calculations
Use the Pythagorean theorem for right-angled triangles: a² + b² = c², where c is the hypotenuse. Show your working for calculation questions. Give units where needed.
Pythagorean Theorem and Basic Calculations
1.Which set of whole-number side lengths makes a right-angled triangle?
- 6, 7, 9
- 5, 12, 13
- 4, 6, 8
- 8, 10, 12
2.A right-angled triangle has shorter sides of 9 cm and 12 cm. Find the hypotenuse.
3.The hypotenuse of a right-angled triangle is 17 cm, and one shorter side is 8 cm. Calculate the length of the other side.
4.A 13 m support cable runs from the ground to a point on a vertical pole. Its ground anchor is 5 m from the base of the pole. How high up the pole does the cable reach?
Problem Solving and Applications
5.A rectangular noticeboard is 40 cm wide and 30 cm high. What is the length of its diagonal?
6.A cyclist travels 8 km west and then 15 km south. How far is the cyclist from the starting point in a straight line?
7.The side lengths of a right-angled triangle are in the ratio 3:4:5. Its perimeter is 72 cm. Find the length of each side, from shortest to longest.
8.A square has a diagonal of 8√2 cm. Calculate its area.
Further Applications
9.A cone is 12 cm high and has a base radius of 5 cm. Find its slant height, measured from the tip to the edge of the base. Treat the height and radius as perpendicular.
10.Two boats leave the same wharf at the same time. One travels east at 12 km/h and the other travels north at 16 km/h. How far apart are they after 3 hours?
11.Show that a triangle with side lengths 9 cm, 40 cm and 41 cm is right-angled. Include the calculation that supports your conclusion.
12.Describe two real-world situations where the Pythagorean theorem could help find a distance that is difficult to measure directly.
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