12 in X?13 4. 17 cm 11.9 cm 28.5 in X 38 in X 32.5 mm 8. 30 mm our equal sides. Each side is 90 feet. 2nd base
The Correct Answer and Explanation is:
Of course. Here are the correct answers and a detailed explanation for the problems shown in the image.
The problems on this worksheet require the use of the Pythagorean theorem. This geometric rule applies to all right-angled triangles and is expressed by the formula a² + b² = c². In this equation, ‘a’ and ‘b’ represent the lengths of the two legs adjacent to the right angle, while ‘c’ represents the length of the hypotenuse, which is the side opposite the right angle. By substituting the known side lengths into this formula, we can solve for the unknown side, labeled ‘x’ in each problem.
Problem 4:
For this problem, we are given the hypotenuse (17 cm) and one leg (11.9 cm). We need to find the other leg (x). The equation is 11.9² + x² = 17². This simplifies to 141.61 + x² = 289. To isolate x², we subtract 141.61 from 289, which gives 147.39. The square root of 147.39 is approximately 12.14.
Answer: x ≈ 12.14 cm
Problem 6:
In problem 6, the unknown side ‘x’ is the hypotenuse. The two legs are 28.5 inches and 38 inches. We use the formula as 28.5² + 38² = x². Calculating the squares gives us 812.25 + 1444 = x². The sum is 2256.25. Therefore, x is the square root of 2256.25, which is exactly 47.5 inches. The handwritten work on the paper appears to have a calculation error leading to an incorrect result.
Answer: x = 47.5 in
Problem 8:
In problem 8, we again solve for a missing leg, ‘x’. The hypotenuse is 32.5 mm, and the known leg is 30 mm. The setup is x² + 30² = 32.5². This becomes x² + 900 = 1056.25. Subtracting 900 from both sides leaves us with x² = 156.25. Taking the square root, we find that x equals 12.5.
Answer: x = 12.5 mm
