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Visual Worksheet: Special Right Triangles | Mathematics (Maths) Class 7 (Old NCERT) PDF Download

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FAQs on Visual Worksheet: Special Right Triangles - Mathematics (Maths) Class 7 (Old NCERT)

1. What are the key properties of 30-60-90 triangles?
Ans. In a 30-60-90 triangle, the sides have a specific ratio: the length of the side opposite the 30-degree angle is \(x\), the side opposite the 60-degree angle is \(x\sqrt{3}\), and the hypotenuse is \(2x\). This ratio is crucial for solving problems involving these triangles.
2. How do you find the lengths of the sides in a 45-45-90 triangle?
Ans. In a 45-45-90 triangle, both legs are of equal length, denoted as \(x\). The hypotenuse is \(x\sqrt{2}\). To find the lengths, if you know the length of one leg, you can easily calculate the hypotenuse using this ratio.
3. Can special right triangles be used in real-life applications?
Ans. Yes, special right triangles are widely used in various real-life applications, such as architecture, engineering, and construction. For instance, they help in determining heights of structures and in creating precise angles for design purposes.
4. How can I quickly remember the ratios of sides in special right triangles?
Ans. A useful mnemonic for the 30-60-90 triangle is "1, \(\sqrt{3}\), 2" corresponding to the angles. For the 45-45-90 triangle, remember "1, 1, \(\sqrt{2}\)." Creating visual aids or flashcards can also help reinforce these ratios.
5. What is the relationship between special right triangles and the Pythagorean theorem?
Ans. Special right triangles exemplify the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This relationship is evident in both 30-60-90 and 45-45-90 triangles, confirming the side length ratios derived from the theorem.
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