Here are five quick questions to help you assess knowledge of right triangles. Each question tests different aspects, such as properties, the Pythagorean theorem, and basic trigonometric ratios.
Questions:
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Identify the Hypotenuse: In a right triangle with legs measuring 6 cm and 8 cm, what is the length of the hypotenuse?
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Pythagorean Theorem: If one leg of a right triangle is 4 units, the other leg is 3 units, verify whether the triangle is a right triangle using the Pythagorean theorem.
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Angle Calculation: If one angle of a right triangle is 30 degrees, what is the measure of the other non-right angle?
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Trigonometric Ratios: In a right triangle, if the opposite side to a 45-degree angle measures 5 units, what is the length of the adjacent side?
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Finding Area: A right triangle has legs measuring 9 cm and 12 cm. What is the area of the triangle?
Answers:
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Answer: Use the Pythagorean theorem \( c = \sqrt{a^2 + b^2} \): \( c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \) cm.
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Answer: Check: \( 4^2 + 3^2 = 16 + 9 = 25\). The square of the hypotenuse should be \( 5^2 = 25\), which matches. Yes, it is a right triangle.
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Answer: The sum of angles in a triangle is 180 degrees. In a right triangle, one angle is 90 degrees. Thus, \( 90 + 30 + x = 180 \) leads to \( x = 60\) degrees.
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Answer: In a 45-degree right triangle, the legs are equal, so the adjacent side is also 5 units.
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Answer: The area \( A \) of a right triangle is calculated as \( A = \frac{1}{2} \times \text{base} \times \text{height}\). Thus, \( A = \frac{1}{2} \times 9 \times 12 = 54 \) cm².
Feel free to modify the questions or use them as a quick review or quiz on right triangles!
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