Question - Calculating the Length of the Hypotenuse in a Right Triangle
Solution:
In this image, we see a right triangle with one side measuring 36 kilometers and another side (which is the opposite of the 90-degree angle) measuring 77 kilometers. The question asks for the length of the hypotenuse, denoted as "c."To find the length of the hypotenuse, we can use the Pythagorean theorem, which 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 formula is:c^2 = a^2 + b^2Here, a = 36 km and b = 77 km, so we have:c^2 = 36^2 + 77^2c^2 = 1296 + 5929c^2 = 7225Taking the square root of both sides gives us the length of the hypotenuse c:c = √7225c ≈ 85Now, rounding to the nearest tenth as requested, we get:c ≈ 85.0 kilometersTherefore, the length of the hypotenuse is approximately 85.0 kilometers.
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