Instructions
Below are some exercises based on Pythagoras' Theorem and triangle geometry. Read each question carefully and show your work. Remember to space out your calculations and double-check your answers.
Exercises
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Calculate the length of the hypotenuse of a right triangle where the other two sides (legs) measure 6 cm and 8 cm.
Formula: c = √(a² + b²)
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If a right triangle has a hypotenuse of 10 cm and one leg measuring 6 cm, find the length of the other leg.
Formula: b = √(c² - a²)
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A triangle has sides measuring 7 cm, 24 cm, and 25 cm. Determine whether this triangle is a right triangle.
Use the Pythagorean Theorem to verify: c² = a² + b² where c is the longest side.
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For a triangle with angles measuring 30°, 60°, and 90°, if the leg opposite the 30° angle is 5 cm, find the lengths of the other two sides.
Hint: Use the properties of special triangles.
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Write a short paragraph explaining the significance of the Pythagorean theorem in real-life applications. Provide at least one example of where it might be used.
Extra Challenge
Find the area of the right triangle from Exercise 1 using the formula: Area = (1/2) × base × height. Use the lengths of the legs as the base and height.