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Trigonometry & Applications Flashcards

7 cards from real Geometry 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. Using the Law of Sines, if a = 8, angle A = 30°, and angle B = 45°, which sets up side b?

    Answer: b = 8 sin 45° / sin 30°

    By the Law of Sines a/sin A = b/sin B, so b = 8 sin 45°/sin 30°.

  2. The Law of Cosines c² = a² + b² − 2ab cos C reduces to the Pythagorean theorem when C equals what?

    Answer: 90°

    At C = 90°, cos C = 0, leaving c² = a² + b².

  3. In triangle with sides a = 5, b = 7 and included angle C = 60°, what is c²?

    Answer: 39

    c² = 25 + 49 − 2(5)(7)(0.5) = 74 − 35 = 39.

  4. What is the area of a triangle with sides 6 and 10 and an included angle of 30°?

    Answer: 15

    Area = ½·6·10·sin 30° = ½·60·0.5 = 15.

  5. When is the Law of Cosines preferred over the Law of Sines?

    Answer: Given SAS or SSS

    The Law of Cosines works directly with SAS or SSS configurations.

  6. In triangle ABC, angle A = 40°, angle B = 60°. What is angle C?

    Answer: 80°

    Angles sum to 180°, so C = 180° − 40° − 60° = 80°.

  7. The ambiguous case (two possible triangles) can occur with which given information?

    Answer: SSA

    SSA can produce zero, one, or two triangles, making it ambiguous.