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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.

Read the first 7 Right Triangles and Trigonometry flashcards as text

  1. In right triangle ABC with right angle at C, AB = 20 and sin(A) = 3/5. What is BC?

    Answer: 12

    sin(A) = BC/AB = BC/20 = 3/5; BC = 12.

  2. A right isosceles triangle has a hypotenuse of 18. What is the area of the triangle?

    Answer: 81

    Legs = 18/√2 = 9√2; area = (1/2)(9√2)(9√2) = (1/2)(162) = 81.

  3. From the base of a hill, a climber walks 200 meters along a slope that makes a 30° angle with the horizontal. How high does the climber rise?

    Answer: 100

    Height = 200 sin(30°) = 200 × 1/2 = 100.

  4. In right triangle JKL with right angle at L, tan(K) = 2. If KL = 5, what is JL?

    Answer: 10

    tan(K) = JL/KL = JL/5 = 2; JL = 10.

  5. A right triangle has a hypotenuse of 10 and one acute angle of 37°. Which expression gives the leg opposite the 37° angle?

    Answer: 10 sin(37°)

    sin(37°) = opposite/hypotenuse; opposite = 10 sin(37°).

  6. Two right triangles share the same hypotenuse of length 26. One has a leg of 10; the other has a leg of 24. Are both valid right triangles?

    Answer: Yes — 10-24-26 and both satisfy the Pythagorean theorem

    10² + 24² = 100 + 576 = 676 = 26²; both 10-24-26 (same triangle, just different legs named) satisfy the theorem.

  7. A 30-60-90 triangle has hypotenuse 22. What is the area of the triangle?

    Answer: (121√3)/2

    Short leg = 11; long leg = 11√3; area = (1/2)(11)(11√3) = (121√3)/2.