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 no solutions, we look for conditions where $b$ does not meet the criteria for forming a valid triangle. This occurs when $b$ is greater than the maximum possible length determined by the given side $a$ and angle $A$, which is when $b$ is greater than $\frac{13}{\sin 24^\circ}$. This means the triangle cannot be formed because side $b$ would be too long to meet with the other sides based on the given angle $A$.

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 $b \leq \frac { 13 } { \sin 24 ^ { \circ } }$