Law of sines: sine of cap A over A is equal to sine of cap b over b is equal to sine of cap c over c In triangle ABC , c is equal to 5 point 4 , A is equal to 3 point 3 , and m angle cap A is equal to 20 degrees What are the possible approximate lengths of b ? Use the law of sines to find the answer.
Answer
A
2 point 0 units and 4 point 6 units
B
2 point 6 units and 6 point 6 units
C
2 point 1 units and 8 point 7 units
D
2 point 3 units and 7 point 8 units
Explanation
Using the Law of Sines, sin C = (5.4 × sin 20°) ÷ 3.3 ≈ 0.560. This gives two possible angles for C: about 34.1° or 145.9°, so angle B is about 125.9° or 14.1°. Then b = (3.3 × sin B) ÷ sin 20°, giving b ≈ 7.8 units or 2.3 units. The possible lengths are 2.3 units and 7.8 units, choice D.
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