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Right Triangles and Trigonometry

SAT Math· difficulty 3/5

If sin⁡θ=513\sin\theta = \frac{5}{13} and θ\theta is acute, what is cos⁡θ\cos\theta?

  • A

    512\frac{5}{12}

  • B

    1312\frac{13}{12}

  • C

    1213\frac{12}{13}

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  • D

    813\frac{8}{13}

Explanation

cos⁡2θ=1−25169=144169\cos^2\theta = 1 - \frac{25}{169} = \frac{144}{169}, so cos⁡θ=1213\cos\theta = \frac{12}{13} (positive for acute).

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