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In a right triangle the two legs are in the ratio 1 : 2. If θ is the smaller acute angle, then sinθ·cosθ equals:

Competition practiceTrigonometry
  • A1/5
  • B2/√5
  • C2/5
  • D4/5

Step-by-Step Solution

Take the legs as 1 and 2, so the hypotenuse is √(1 + 4) = √5. The smaller angle faces the shorter leg, giving sinθ = 1/√5 and cosθ = 2/√5, so the product is 2/5 = 0.4 (here θ ≈ 26.57°). The distractors are the pieces of that calculation: 1/5 is siθ, 4/5 is coθ and 2/√5 is cosθ on its own.
Answer: C) 2/5

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