Question - Calculating the Hypotenuse of a Right Triangle
Solution:
$$c^2 = a^2 + b^2$$$$c^2 = 3^2 + 4^2$$$$c^2 = 9 + 16$$$$c^2 = 25$$$$c = \sqrt{25}$$$$c = 5$$
Tutor Solution:
To find the hypotenuse $$ c $$ of a right triangle when the lengths of the other two legs, $$ a $$ and $$ b $$, are known, we use the Pythagorean theorem. The Pythagorean theorem states:\[ c^2 = a^2 + b^2 \]Given in the problem, the lengths of the legs $$ a $$ and $$ b $$ are:\[ a = 3 \]\[ b = 4 \]We plug these values into the Pythagorean theorem:\[ c^2 = 3^2 + 4^2 \]\[ c^2 = 9 + 16 \]\[ c^2 = 25 \]To solve for $$ c $$, we take the square root of both sides:\[ c = \sqrt{25} \]\[ c = 5 \]Therefore, the hypotenuse $$ c $$ of the right triangle with legs $$ a = 3 $$ and $$ b = 4 $$ is 5.
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