Topic Details (Notes format)

How to Calculate the Area of Any Triangle Using Trigonometry

Subject: Mathematics

Book: Maths Mastery

For a general triangle with sides a, b and included angle C, the area formula is (1/2)ab sin(C). If you have a=8, b=10, and C=60°, the area is 0.5 × 8 × 10 × sin(60°) = 40 × (√3/2) = 20√3. This approach bypasses perpendicular height by utilizing trigonometric ratios. Applicable in surveying or design, it ensures you can swiftly compute areas without rearranging or dropping altitudes. Mastering this technique broadens your repertoire for geometry problem-solving where direct height measures aren’t readily available.

Practice Questions

A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If a square has a perimeter of 64 cm, what is its area?

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What is the area of an equilateral triangle with side length 10 cm?

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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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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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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 area of a circle with a diameter of 14 cm?

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The LCM of 12 and 15 is:

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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