Free SAT Practice Question

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ID: SAT-MATH-GT-025
Section: SAT Math - Geometry & Trigonometry (G&T)
Topic: Right triangles and trigonometry
Difficulty level: Hard

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In triangle \(ABC\), the angle at \(C\) is a right angle. Point \(D\) lies on side \(\overline{CB}\) between \(C\) and \(B\). The measure of angle \(BAC\) is \(60^\circ\), the measure of angle \(DAC\) is \(45^\circ\), and \(AC = 6\). What is the length of \(\overline{BD}\) ?

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