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Lines, Angles, and Triangles

SAT Math· difficulty 5/5

In right triangle ABC with the right angle at C, tanA=frac34\\tan A = \\frac{3}{4} and AC=8AC = 8. What is the length of AB?

  • A

    323\frac{32}{3}

  • B

    73\sqrt{73}

  • C

    12

  • D

    10

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Explanation

tanA=fracBCAC=frac34\\tan A = \\frac{BC}{AC} = \\frac{3}{4}. So BC=6BC = 6. Then AB=sqrt82+62=sqrt100=10AB = \\sqrt{8^2 + 6^2} = \\sqrt{100} = 10 (3-4-5 scaled).

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