Example Question - triangle side calculation
Here are examples of questions we've helped users solve.
Finding Missing Side Length in Right Triangle using Pythagorean Theorem
The Pythagorean theorem is used to find the length of a side of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as: a² + b² = c² Here, c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. From the image, the hypotenuse of the triangle is 17 inches, and one of the other sides is 8 inches. We need to find the length of the missing side, labeled b. Using the Pythagorean theorem: 8² + b² = 17² 64 + b² = 289 Now, subtract 64 from both sides to isolate b²: b² = 289 - 64 b² = 225 Taking the square root of both sides gives us the length of the missing side: b = √225 b = 15 Therefore, the length of the missing side b is 15 inches.
Calculating the Length of the Third Leg in a Right Triangle
The image shows a right triangle with one leg of length 7, the hypotenuse of length 9, and the other leg (which we want to find) labeled 'x'. To solve for 'x', we can use the Pythagorean theorem, which states that for a right triangle with legs 'a' and 'b', and hypotenuse 'c', the following equation holds true: a² + b² = c² Here, 'a' is 7, 'b' is 'x', and 'c' is 9. Plugging in the values we have: 7² + x² = 9² 49 + x² = 81 Now we'll solve for x²: x² = 81 - 49 x² = 32 Taking the square root of both sides to solve for 'x': x = √32 Now we can calculate the value of 'x' and round it to the nearest tenth: x ≈ 5.7 So, 'x' rounded to the nearest tenth is approximately 5.7.
Solving for the Length of a Right Triangle Leg
The image shows a right triangle, with one leg measuring 10 feet and the hypotenuse measuring 45 feet. To solve for the length of the other leg of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b² Here, we know the hypotenuse (c) is 45 feet and one leg (a) is 10 feet. We need to find the length of the other leg (b): 45² = 10² + b² 2025 = 100 + b² 2025 - 100 = b² 1925 = b² Now, we take the square root of both sides to find the length of the unknown side (b): b = √1925 b ≈ 43.86 feet The length of the other leg is approximately 43.86 feet.
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