In a triangle △ABC, the ∠ABC = 90°. If sin(A) = 1⁄2, then cos(C) is equal to:
Step 1: Understand the given information
We have a right triangle △ABC where ∠ABC = 90°, and sin(A) = 1⁄2. By definition,
sin(A) = Opposite side ÷ Hypotenuse.
Step 2: Assign sides based on sin(A)
Let the hypotenuse = 2 and the opposite side to ∠A = 1 (since sin(A) = 1 ÷ 2).
Step 3: Find the adjacent side using Pythagoras theorem
Hypotenuse2 = Opposite2 + Adjacent2
22 = 12 + Adjacent2
4 = 1 + Adjacent2
Adjacent2 = 3
Adjacent = √3.
Step 4: Calculate cos(C)
For ∠C, cos(C) = Adjacent side (to ∠C) ÷ Hypotenuse.
Adjacent to ∠C = 1, Hypotenuse = 2.
cos(C) = 1⁄2.
Thus, the correct answer is (4), 1⁄2.
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