Question - Calculating the Length of the Hypotenuse of a Right Triangle
Solution:
The triangle shown in the image is a right triangle, and we are looking for the length of the hypotenuse, denoted as "c". According to the Pythagorean theorem, in a right 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. This can be written as:c² = a² + b²wherec = length of the hypotenuse,a and b = lengths of the other two sides of the right triangle.From the image, we have:a = 60 meters,b = 80 meters.Now we plug these values into the Pythagorean theorem:c² = 60² + 80²c² = 3600 + 6400c² = 10000To find c, we take the square root of both sides:c = √10000c = 100Therefore, the length of the hypotenuse is 100 meters. Since the problem states that we should round to the nearest tenth if necessary, we can express our final answer as 100.0 meters, although it is not required in this case since 100 is a whole number.
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