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A triangle has sides of 12 and 10 with an included angle of 30 degrees. What is its area?
A30 square units
B60 square units
C15 square units
D120 square units
Answer & Solution
Correct answer: A. 30 square units
1. The area is one half of the product of two sides and the sine of their included angle.
2. The sine of 30 degrees is 0.5.
3. So the area is 0.5 times 12 times 10 times 0.5.
4. That gives 30 square units.
5. Answering 60 square units forgets the leading one half in the formula.
_Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.1 Non-right Triangles: Law of Sines_