Find values for b such that the triangle has no solutions. A = 64°, a = 340.2 A) $b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }$ B) $b = \frac { 340.2 } { \sin 64 ^ { \circ } }$ C) $b \geq \frac { 340.2 } { \sin 64 ^ { \circ } }$ D) $b \frac { 340.2 } { \sin 64 ^ { \circ } }$

Question

Find values for b such that the triangle has no solutions.  
A = 64°, a = 340.2
 
A) $b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }$
B) $b = \frac { 340.2 } { \sin 64 ^ { \circ } }$
C) $b \geq \frac { 340.2 } { \sin 64 ^ { \circ } }$
D) $b < \frac { 340.2 } { \sin 64 ^ { \circ } }$
E) $b > \frac { 340.2 } { \sin 64 ^ { \circ } }$

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 sine of that angle and the given side length. Thus, if $b > \frac{340.2}{\sin 64^\circ}$, it implies that side b is too long to form a triangle with the given dimensions, leading to no possible triangle.

Find Values for B Such That the Triangle Has No b≤340.2sin⁡64∘b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }b≤sin64∘340.2​

Find Values for B Such That the Triangle Has No $b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }$