Question - Calculating the Length of the Hypotenuse of a Right-Angled Triangle
Solution:
The image displays a right-angled triangle with the two legs measuring 60 meters and 80 meters, and the length of the hypotenuse labeled as "c." To find the length of the hypotenuse, we use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.The Pythagorean theorem is expressed as:\[ c^2 = a^2 + b^2 \]where $$ c $$ is the length of the hypotenuse, and $$ a $$ and $$ b $$ are the lengths of the other two sides.Given the side lengths of 60 meters and 80 meters, we can plug them into the equation:\[ c^2 = 60^2 + 80^2 \]\[ c^2 = 3600 + 6400 \]\[ c^2 = 10000 \]To find $$ c $$, we take the square root of both sides of the equation:\[ \sqrt{c^2} = \sqrt{10000} \]\[ c = 100 \]Thus, the length of the hypotenuse is 100 meters. There is no need to round to the nearest tenth, since we have an exact value.
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