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Right Triangles and Trigonometry Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. In right triangle ABC with the right angle at C, AB = 17 and BC = 8. What is the value of tan(A)?

    Answer: 8/15

    AC = √(17² − 8²) = √(289 − 64) = √225 = 15; tan(A) = opposite/adjacent = BC/AC = 8/15.

  2. A right triangle has a hypotenuse of 26 and one leg of 10. What is the length of the other leg?

    Answer: 24

    Other leg = √(26² − 10²) = √(676 − 100) = √576 = 24.

  3. A ramp rises 5 feet over a horizontal distance of 12 feet. What is the length of the ramp?

    Answer: 13

    Ramp length = √(5² + 12²) = √(25 + 144) = √169 = 13.

  4. In a right triangle, one acute angle measures 30°. The side opposite this angle is 7. What is the length of the hypotenuse?

    Answer: 14

    sin(30°) = 1/2 = opposite/hypotenuse = 7/hyp; hyp = 14.

  5. A 45-45-90 triangle has legs of length 9. What is the perimeter of the triangle?

    Answer: 18 + 9√2

    Hypotenuse = 9√2; perimeter = 9 + 9 + 9√2 = 18 + 9√2.

  6. In right triangle XYZ with the right angle at Z, cos(X) = 5/13. What is sin(X)?

    Answer: 12/13

    sin²(X) + cos²(X) = 1; sin(X) = √(1 − 25/169) = √(144/169) = 12/13.

  7. Two similar right triangles have corresponding hypotenuses of 10 and 25. If the shorter triangle has a leg of 6, what is the corresponding leg of the larger triangle?

    Answer: 15

    Scale factor = 25/10 = 2.5; corresponding leg = 6 × 2.5 = 15.