State whether the given measurements determine zero, one, or two triangles.
-$$\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 28 , \mathrm { c } = 30$$
A) Zero
B) One
C) Two

Question

Quizplus · Accepted Answer

Given C = 35°, a = 28, and c = 30, we use the Law of Sines to determine if there is a solution. Since a < c and C is acute, there is at least one solution. To check for a second solution, we need to see if an angle supplementary to the one we find would still result in a valid triangle. However, since a < c, there is no angle ambiguity, leading to only one possible triangle.

State Whether the Given Measurements Determine Zero, One, or Two C=35∘,a=28,c=30\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 28 , \mathrm { c } = 30C=35∘,a=28,c=30

State Whether the Given Measurements Determine Zero, One, or Two $\mathrm { C } = 35 ^ { \circ } , \mathrm { a } = 28 , \mathrm { c } = 30$