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

If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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What is the cube root of 729?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the value of log₃(27)?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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