Select a value for b such that a triangle with A = 33° and a = 4 has no solution.
A)1.84
B)3.67
C)7.24
D)14.68
E)1.47

Question

Select a value for b such that a triangle with A = 33° and a = 4 has no solution. 
A)1.84 
B)3.67 
C)7.24 
D)14.68 
E)1.47

Quizplus · Accepted Answer

According to the sine law, $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$. Since $a$ and $A$ are fixed, we can find the range of possible values for $\sin B$ by rearranging the sine law as follows: $$\sin B=\dfrac{b\sin A}{a}.$$ Then we know that $0<\sin B\leq 1$. If we plug in the given values, we get $$0<\sin B\leq\dfrac{b\sin 33^\circ}{4}.$$ By choosing $b$ to be greater than or equal to $\dfrac{4}{\sin 33^\circ}\approx 7.24$, we ensure that $\sin B$ cannot be greater than 1, and so there are no possible triangles. Only choice D satisfies this condition.

Select a Value for B Such That a Triangle with a =