Cassandra assigns values to some of the measures of triangle ABC . If angle cap A measures 30° , A is equal to 6 , and b is equal to 18 , which is true?
Answer
A
The triangle does not exist because sine cap A over A cannot equal sine cap b over b .
B
There is one non-right triangle that can be created with those measures because A is less than b .
C
There are two non-right triangles that can be created with those measures because A is less than b comma b is less than cap A .
D
The triangle is a right triangle because times 3 is , and 6 times 3 is 18 .
Explanation
By the Law of Sines, sin B / b must equal sin A / a. Substituting the given values gives sin B = (18 × sin 30°) / 6 = 1.5. Since a sine value cannot be greater than 1, no triangle can have these measurements, so the statement that the triangle does not exist is true.
AI-written and checked against the verified answer.