In a right triangle, let a and b represent the legs and c the hypotenuse. If α is the angle opposite a, which of the following relations is true?
A) a = c sin(α)
B) c = a sin(α)
C) a = b cos(α)
D) a = c cos(α)
E) c = a cos(α)
IMAT 2024 · Question 54
Q54 - Sine, cosine and tangent
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The correct answer is A) a = c sin(α).
In a right triangle, sin α = opposite / hypotenuse = a / c, so a = c sin α.
B and E would make the hypotenuse shorter than a leg, which is impossible. D gives the other leg, b, since cos α = b/c.
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