Question - Finding the Missing Side of a Right Triangle
Solution:
The image shows a right triangle with one side labeled 9, the hypotenuse labeled 18, and the other side labeled x. To find the missing side labeled x, we will use the Pythagorean theorem, which states that for a right-angled triangle $$ a^2 + b^2 = c^2 $$, where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse.Let's solve for x:Given that one leg is 9 and the hypotenuse c, is 18:\[ a^2 + b^2 = c^2 \]\[ 9^2 + x^2 = 18^2 \]\[ 81 + x^2 = 324 \]Now, isolate x^2 by subtracting 81 from both sides:\[ x^2 = 324 - 81 \]\[ x^2 = 243 \]Next, find the square root of both sides to solve for x:\[ x = \sqrt{243} \]\[ x = 15.588 \] (rounded to three decimal places)So, the missing side labeled x is approximately 15.588 units long. However, depending on the context or instructions given, you may need to round this to a different number of decimal places or provide an exact answer in the form of a square root.
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