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 a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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If two complementary angles differ by 30°, what are the angles?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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The LCM of 12 and 15 is:

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What is the sum of all even numbers between 1 and 100?

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What is the probability of drawing an ace from a standard deck of 52 cards?

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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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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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