Question - Solving for the Length of a Side in a Right-Angled Triangle
Solution:
The image shows a right-angled triangle with sides labeled. The hypotenuse is labeled as 73, one leg is labeled as 48, and the other leg, which is opposite the right angle, is labeled with the variable N. To solve for N, we can use the Pythagorean theorem, which states that in a right-angled 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 Pythagorean theorem formula is as follows:c² = a² + b²In this case:c = 73 (the hypotenuse),a = 48 (one of the other sides),b = N (the side we're trying to find).Plugging the numbers we know into the formula gives us:73² = 48² + N²Now calculate each term:73² = 5329,48² = 2304,And putting them into the equation:5329 = 2304 + N²Next, subtract 2304 from both sides to solve for N²:5329 - 2304 = N²3025 = N²Finally, take the square root of both sides to find N:N = √3025N = 55Therefore, the value of N is 55.
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