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 x^2 - 5x + 6 = 0, what are the roots?

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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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If x:y = 2:3 and z:y = 4:3, what is x:z?

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If 2x = 16, what is the value of x?

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How many ways can 4 people sit in a row?

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If x^2 - 6x + 9 = 0, what is the value of x?

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What is the sum of the first 20 odd numbers?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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

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

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