Determine the number of triangles ABC possible with the given parts.
-$$a = 24 , b = 21 , A = 47 ^ { \circ }$$
A) 3
B) 2
C) 0
D) 1

Question

Quizplus · Accepted Answer

Given $a = 24$, $b = 21$, and $A = 47^\circ$, we use the Law of Sines to determine the number of possible triangles. The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B}$. We can solve for $\sin B$ to determine if there are 0, 1, or 2 possible triangles. Since $a > b$ and $A < 90^\circ$, there is only one possible triangle because the angle $B$ opposite the shorter side $b$ cannot be obtuse, ensuring a unique solution.

Determine the Number of Triangles ABC Possible with the Given a=24,b=21,A=47∘a = 24 , b = 21 , A = 47 ^ { \circ }a=24,b=21,A=47∘

Determine the Number of Triangles ABC Possible with the Given $a = 24 , b = 21 , A = 47 ^ { \circ }$