Find values for b such that the triangle has one solution.
A = 24°, a = 16.2

Question

Find values for b such that the triangle has one solution. ​
A = 24​°, a = 16.2
​

Quizplus · Accepted Answer

In a triangle, the sine rule states that a/sin(A) = b/sin(B) = c/sin(C). 
So, in this case, we have b/sin(B) = a/sin(A) = 16.2/sin(24°). 
For a triangle to have only one solution, the given angle and side must make sense together. 
This means that b cannot be greater than or equal to 16.2/sin(24°) (otherwise there would be two possible triangles). 
Using a calculator, we get that 16.2/sin(24°) ≈ 40.7. 
So, b must be less than 40.7 to ensure a unique solution. 
Option B, 35, satisfies this condition and hence is the correct answer.

Find Values for B Such That the Triangle Has One