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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 XYZ with right angle at Z, XY = 25 and YZ = 7. What is cos(Y)?

    Answer: 7/25

    cos(Y) = adjacent/hypotenuse = YZ/XY = 7/25.

  2. A 30-60-90 triangle has the longer leg equal to 9√3. What is the length of the shorter leg?

    Answer: 9

    Longer leg = short leg × √3 = 9√3; short leg = 9.

  3. A wire is attached from the top of a 30-foot pole to a stake 16 feet from the base. How long is the wire?

    Answer: 34

    Wire² = 30² + 16² = 900 + 256 = 1156; wire = 34.

  4. In right triangle DEF with right angle at F, tan(D) = 3/4 and EF = 9. What is DE?

    Answer: 15

    tan(D) = EF/DF = 9/DF = 3/4; DF = 12; DE = √(9² + 12²) = √225 = 15.

  5. Two right triangles are similar. Their areas are 50 and 200 square units. What is the ratio of their corresponding sides?

    Answer: 1:2

    Area ratio = 50:200 = 1:4; side ratio = √(1/4) = 1:2.

  6. A right triangle has an acute angle of 60° and the side adjacent to that angle is 5. What is the hypotenuse?

    Answer: 10

    cos(60°) = 1/2 = adjacent/hypotenuse = 5/hyp; hyp = 10.

  7. In right triangle PQR with right angle at R, angle P = 45°. If PQ = 8√2, what is QR?

    Answer: 8

    45-45-90: legs = hyp/√2 = 8√2/√2 = 8.