Topic Details (Notes format)

How to Use the Pythagorean Theorem

Subject: Mathematics

Book: Maths Mastery

The Pythagorean Theorem, a² + b² = c², applies to right-angled triangles, where c represents the hypotenuse (longest side) and a, b are the legs. For instance, if a = 3 cm and b = 4 cm, c = √(3² + 4²) = √25 = 5 cm. This theorem underlies trigonometry, enabling distance calculations in navigation, construction, and design. From verifying corners in building layouts to analyzing diagonal distances on a computer screen, Pythagoras’s principle is indispensable in geometry and everyday spatial reasoning.

Practice Questions

What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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What is the HCF of 72 and 120?

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What is the cube of 4?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If 8x = 512, what is the value of x?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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