Pythagoras Theorem

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Use Pythagoras Theorem: AC^2 = AB^2 + BC^2. Step 1: 6^2 + 8^2 = 36 + 64 = 100. Step 2: AC = √100 = 10 cm. Answer: 10 cm.

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Model the situation as a right triangle. Step 1: Hypotenuse = 13 m, base = 5 m. Step 2: Height^2 = 13^2 - 5^2 = 169 - 25 = 144. Step 3: Height = √144 = 12 m. Answer: 12 m.

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The path makes a right triangle. Step 1: Distance^2 = 40^2 + 50^2. Step 2: = 1600 + 2500 = 4100. Step 3: Distance = √4100 = 10√41 m. Answer: 10√41 m.

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Use Pythagoras Theorem. Step 1: Other side^2 = 15^2 - 9^2. Step 2: = 225 - 81 = 144. Step 3: Other side = √144 = 12 cm. Answer: 12 cm.

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Take the largest side as 5 cm. Step 1: 3^2 + 4^2 = 9 + 16 = 25. Step 2: 5^2 = 25. Step 3: Since the squares are equal, the triangle is right-angled. Answer: Yes, it is a right-angled triangle.

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Use it in a right-angled triangle when two sides are known and the third side is required. Example: If the legs are 8 cm and 15 cm, then hypotenuse^2 = 8^2 + 15^2 = 64 + 225 = 289, so hypotenuse = 17 …

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Formula: AC^2 = AB^2 + BC^2, where AC is the hypotenuse and AB, BC are the other two sides. Example: If AB = 7 cm and BC = 24 cm, then AC^2 = 7^2 + 24^2 = 49 + 576 = 625, so AC = 25 cm.

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The side opposite the 90° angle stretches across the triangle, so it must be longer than each of the other two sides. Example: In a 5 cm, 12 cm, 13 cm triangle, 13 cm is the hypotenuse and the largest…