Question - Solving for the Hypotenuse of a Right Triangle
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Solution:
The image shows a right triangle with sides of length 9 and 15, and you are asked to solve for the length of the hypotenuse, denoted by x. This is an application of the Pythagorean theorem, which states that in a right-angled 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. The formula is given by:$$ x^2 = a^2 + b^2 $$where $$ x $$ is the length of the hypotenuse, and $$ a $$ and $$ b $$ are the lengths of the other two sides.For the given triangle,$$ x^2 = 9^2 + 15^2 $$$$ x^2 = 81 + 225 $$$$ x^2 = 306 $$To find x, take the square root of both sides:$$ x = \sqrt{306} $$When you calculate this value, you get:$$ x \approx 17.5 $$Rounding to the nearest tenth, the length of the hypotenuse $$ x $$ is approximately 17.5.
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