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 How many distinct triangles can be formed for which m angle cap A is equal to 75 degrees , A is equal to 2 , and b is equal to 3 ?
Answer
A
Two triangles can be formed where angle cap b is 40 degrees or 140 degrees .
B
No triangles can be formed.
C
One triangle can be formed where angle cap b is about 40 degrees .
D
One triangle can be formed where angle cap b is about 15 degrees .
Explanation
By the Law of Sines, sin B / 3 = sin 75° / 2, so sin B = (3/2)sin 75° ≈ 1.45. A sine value cannot be greater than 1, so no angle B can satisfy this equation and no triangle can be formed. The correct choice is “No triangles can be formed.”
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