In a triangle ΔABC, the angle ∠ABC = 90°. If sin(A) = 1/2, then find the value of cos(C).

Question

Accepted Answer

Given that ∠ABC = 90°, triangle ABC is a right triangle with B as the right angle. Therefore, angles A and C are complementary, i.e., A + C = 90°. Given sin(A) = 1/2, we know that sin(30°) = 1/2, so angle A = 30°. Since A + C = 90°, angle C = 90° - 30° = 60°. Now, cos(C) = cos(60°) = 1/2. However, the options include √3/2 as well, so let's verify carefully.

Wait, the calculation shows cos(60°) = 1/2, which matches option 4. But option 3 is marked as correct. Let's double-check.

Step 1: ∠B = 90°
Step 2: sin(A) = 1/2 → A = 30°
Step 3: Since sum of angles in triangle = 180°, C = 180° - 90° - 30° = 60°
Step 4: cos(C) = cos(60°) = 1/2

Therefore, the correct answer is 1/2 (option 4).

Answer

Answer

Answer