Question - Solving for Hypotenuse Length in a Right Triangle
Solution:
To solve for the length of the hypotenuse in a right triangle, you 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). The Pythagorean theorem is written as:\[ c^2 = a^2 + b^2 \]According to the image, one leg (a) is 36 km long, and the other leg (b) is 77 km long. We are solving for the hypotenuse (c). Plugging the values into the theorem:\[ c^2 = (36)^2 + (77)^2 \]\[ c^2 = 1296 + 5929 \]\[ c^2 = 7225 \]Now, take the square root of both sides to solve for c:\[ c = \sqrt{7225} \]\[ c = 85 \]Therefore, the length of the hypotenuse is 85 km. Since the question did not ask for rounding unless necessary and we got an exact whole number, we don't round the answer. It is exactly 85 kilometers.
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