Question - Calculation of Hypotenuse in a Right-Angled Triangle
Solution:
The image portrays a right-angled triangle with one leg measuring 60 meters and the other leg measuring 80 meters. To find the length of the hypotenuse (`c`), we would use the Pythagorean theorem. The theorem states that in a right-angled 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 (the legs). The formula is:\[ c^2 = a^2 + b^2 \]where `a` and `b` are the lengths of the legs, and `c` is the length of the hypotenuse.Here, `a = 60 m` and `b = 80 m`, so we plug these values into the formula to get:\[ c^2 = (60)^2 + (80)^2 \]\[ c^2 = 3600 + 6400 \]\[ c^2 = 10000 \]To find `c`, we take the square root of both sides:\[ c = \sqrt{10000} \]\[ c = 100 \]Therefore, the length of the hypotenuse, `c`, is 100 meters. There is no need to round since the result is a whole number.
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