Pythagoras Theroem

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Step 1: Since angle A = 90°, BC is the hypotenuse. Step 2: Use Pythagoras theorem: BC^2 = AB^2 + AC^2. Step 3: BC^2 = 8^2 + 6^2 = 64 + 36 = 100. Step 4: BC = sqrt(100) = 10 cm. Answer: BC = 10 cm.

Answer

Step 1: Since angle Z = 90°, XY is the hypotenuse. Step 2: Use Pythagoras theorem: XY^2 = XZ^2 + YZ^2. Step 3: 15^2 = 9^2 + YZ^2. Step 4: 225 = 81 + YZ^2. Step 5: YZ^2 = 225 - 81 = 144. Step 6: YZ = s…

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Step 1: Since angle R = 90°, PQ is the hypotenuse. Step 2: Use Pythagoras theorem: PR^2 + QR^2 = PQ^2. Step 3: PR^2 + 20^2 = 25^2. Step 4: PR^2 + 400 = 625. Step 5: PR^2 = 625 - 400 = 225. Step 6: PR …

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Step 1: Take the largest side, 20 cm. Step 2: Compare squares: 20^2 and 9^2 + 12^2. Step 3: 20^2 = 400. Step 4: 9^2 + 12^2 = 81 + 144 = 225. Step 5: 400 is not equal to 225. Answer: The triangle is no…

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Step 1: Compare the square of the largest side with the sum of the other two squares. Step 2: Since AB^2 = AC^2 + BC^2, the converse of Pythagoras theorem applies. Step 3: The angle opposite AB is a r…

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Use it in a right-angled triangle to find a missing side. Example: If AB = 8 cm, AC = 6 cm, and angle A = 90°, then BC^2 = 8^2 + 6^2 = 100. So BC = 10 cm. Answer: Use it when one angle is 90° and one …

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In a right-angled triangle, the side opposite the 90° angle is the longest side. That side is called the hypotenuse. Example: If angle A = 90° in triangle ABC, then BC is opposite A, so BC is the hypo…

Answer

Step 1: The hypotenuse is opposite the 90° angle. Step 2: Angle BAC = 90°, so the opposite side is BC. Answer: BC is the hypotenuse.