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A triangle of area 30 square units has one side of 12 and an included angle of 30 degrees. How long is the other side?
AIt is 5 units long
BIt is 10 units long
CIt is 20 units long
DIt is 12 units long
Answer & Solution
Correct answer: B. It is 10 units long
1. The area equals one half times the two sides times the sine of the included angle.
2. Write it as 30 equals 0.5 times 12 times b times the sine of 30 degrees.
3. The sine of 30 degrees is 0.5.
4. So 30 equals 0.5 times 12 times b times 0.5.
5. The constants multiply to 3, giving 30 equals 3b.
6. Dividing by 3 gives b equal to 10 units.
7. Answering 5 units drops the one half and solves 30 equals 6b instead.
8. Answering 20 units forgets the sine factor and solves 30 equals 6b the other way.
9. Answering 12 units simply repeats the side that was already given.
_Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.1 Non-right Triangles: Law of Sines_