In right triangle ABC, the right angle is at A, m∠B = 30°, m∠C = 60°, and the hypotenuse BC = 20. What is the area of △ABC?
A173.21 sq. units
B100 sq. units
C86.6 sq. units
D150 sq. units
Explanation
In a 30-60-90 triangle, the side opposite 30° (short leg, AC) = hypotenuse/2 = 10.0. The side opposite 60° (long leg, AB) = short leg × √3 = 17.32. Area = ½ × 10.0 × 17.32 = 86.6 sq. units.
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