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

To have no solution for a triangle with A = 33° and a = 4, we need b to be greater than or equal to 8. This can be found using the sine rule: b/sin(B) = a/sin(A), where B is the angle opposite side b. Solving for sin(B), we get sin(B) = (b*sin(A))/a. Since sin(B) must be less than or equal to 1, we can solve for the maximum value of b: b = (a*sin(B))/sin(A). Plugging in the given values, we get b = (4*sin(B))/sin(33°). By testing the answer choices, we find that b = 14.68 is the smallest value that makes b greater than or equal to 8, so there will be no solution for a triangle with A = 33° and a = 4 if b = 14.68.

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