Determine the number of triangles ABC possible with the given parts.
-$$\mathrm { a } = 24 , \mathrm {~b} = 19 , \mathrm {~A} = 43 ^ { \circ }$$
A) 0
B) 3
C) 2
D) 1

Question

Quizplus · Accepted Answer

Given $a = 24$, $b = 19$, and $A = 43^\circ$, we can use the Law of Sines to determine the possible number of triangles. The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B}$. We can solve for $\sin B$ to see if it yields a valid value (i.e., $-1 \leq \sin B \leq 1$). Since there is only one angle $A$ and the given sides $a$ and $b$ do not suggest an ambiguous case (where $b$ is not long enough to reach side $a$ after swinging down from the angle $A$), there is only one possible triangle.

Determine the Number of Triangles ABC Possible with the Given a=24, b=19, A=43∘\mathrm { a } = 24 , \mathrm {~b} = 19 , \mathrm {~A} = 43 ^ { \circ }a=24, b=19, A=43∘

Determine the Number of Triangles ABC Possible with the Given $\mathrm { a } = 24 , \mathrm {~b} = 19 , \mathrm {~A} = 43 ^ { \circ }$