To find the length of segment \(AD\) in right triangle \(ABC\) with altitude \(CD\), we can utilize the properties of similar triangles and the Pythagorean theorem.
Assuming that we have the lengths of the sides of the triangle or some necessary dimensions given in the image (which I cannot see), here's how you can generally approach the problem:
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Identify the Similar Triangles: In triangle \(ABC\), the altitude \(CD\) creates two smaller right triangles \(ACD\) and \(BCD\) that are similar to triangle \(ABC\).
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Use Similar Triangles: If \(AB\) is the hypotenuse of triangle \(ABC\) and \(AC\) and \(BC\) are the other two sides, you can set up the ratios based on their corresponding sides: \[ \frac{AD}{AC} = \frac{CD}{AB} \quad \text{and} \quad \frac{BD}{BC} = \frac{CD}{AB} \]
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Pythagorean Theorem: You can also apply the Pythagorean theorem to each smaller triangle: \[ AC^2 = AD^2 + CD^2 \] \[ BC^2 = BD^2 + CD^2 \]
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Express Unknowns: If you know the lengths of \(AC\) and \(BC\), and if you can set up \(AB\) as \(AD + BD\), you may express all needed segments in terms of one variable.
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Solve for AD: After substituting everything in terms of a single variable, you can solve for \(AD\) and round it to two decimal places as needed.
If you provide specific lengths or values involved, I could help with more detailed calculations!
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