Question - Solving for the Length of a Right Triangle Side
Solution:
The image displays a right-angled triangle with one leg labeled as 12, the hypotenuse labeled as 26, and the other leg labeled as $$x$$. To solve for $$x$$, we can use the Pythagorean theorem, which states for a right-angled triangle that $$a^2 + b^2 = c^2$$, where $$a$$ and $$b$$ are the lengths of the legs and $$c$$ is the length of the hypotenuse.Given:$$a = x$$ (the unknown side we are trying to find)$$b = 12$$ (one of the legs)$$c = 26$$ (the hypotenuse)The equation becomes:$$x^2 + 12^2 = 26^2$$Now we can solve for $$x$$:$$x^2 + 144 = 676$$Subtract 144 from both sides to isolate $$x^2$$:$$x^2 = 676 - 144$$$$x^2 = 532$$Now take the square root of both sides to solve for $$x$$:$$x = \sqrt{532}$$$$x$$ is the square root of 532, which can be simplified:$$x = \sqrt{4 \cdot 133}$$$$x = \sqrt{4} \cdot \sqrt{133}$$$$x = 2 \cdot \sqrt{133}$$So the length of the unknown side $$x$$ is $$2\sqrt{133}$$, which is an exact value. If a decimal value is required, you would need to use a calculator to approximate the square root of 133.
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