Find values for b such that the triangle has one solution.
A = 62°, a = 304.6

Question

Find values for b such that the triangle has one solution. ​
A = 62°, a = 304.6
​

Quizplus · Accepted Answer

In a triangle, the sine rule states that a/sin A = b/sin B = c/sin C. If A = 62° and a = 304.6, we can calculate the value of sin A:
sin A = (a/ b) / sin B
sin A = (304.6/ b) / sin B
sin A = 304.6 / (b x sin B)
sin A ≈ 0.866
Using the inverse sine function, we find that B ≈ 59.3°. Now, the sum of angles in a triangle is 180°, so we can calculate C:
C = 180° - A - B
C ≈ 58.7°
Finally, we can use the sine rule again to find the value of c:
c/sin C = a/sin A
c/sin 58.7° = 304.6 / sin 62°
c ≈ 309.8
Therefore, there is only one solution for the triangle when b is greater than or equal to approximately 309.8. The best choice is D, as it has the highest value for b.

Find Values for B Such That the Triangle Has One