Find values for b such that the triangle has no solutions. A = 24°, a = 13 A) $b \leq \frac { 13 } { \sin 24 ^ { \circ } }$ B) $b \frac { 13 } { \sin 24 ^ { \circ } }$ C) $b = \frac { 13 } { \sin 24 ^ { \circ } }$ D) $b

Question

Find values for b such that the triangle has no solutions.  
A = 24°, a = 13
 
A)  $b \leq \frac { 13 } { \sin 24 ^ { \circ } }$
B) $b > \frac { 13 } { \sin 24 ^ { \circ } }$
C) $b = \frac { 13 } { \sin 24 ^ { \circ } }$
D) $b < \frac { 13 } { \sin 24 ^ { \circ } }$
E) $b \geq \frac { 13 } { \sin 24 ^ { \circ } }$

Quizplus · Accepted Answer

For a triangle to have no solutions in the context of the Law of Sines, the side opposite the given angle must be shorter than the product of the other given side and the sine of the given angle. However, since the question asks for when the triangle has no solutions, we look for when the opposite is true: when $b$ is greater than the product of $a$ and the sine of angle $A$, meaning $b > \frac{13}{\sin 24^\circ}$. This condition implies that the specified side $b$ is too long to form a triangle given the angle $A = 24^\circ$ and side $a = 13$.

Find Values for B Such That the Triangle Has No b≤13sin⁡24∘b \leq \frac { 13 } { \sin 24 ^ { \circ } }b≤sin24∘13​

Find Values for B Such That the Triangle Has No $b \leq \frac { 13 } { \sin 24 ^ { \circ } }$