Question

How do you determine the number of possible solutions to solve triangle ABC if `A=30^circ`, b=18.6, and a=9.3?

Answer 1

There is exactly one solution.

Explanation:

Given
`color(white)("XXX")/_BAC=30^@`
and
`color(white)("XXX")abs(AC)=18.6`

The minimum distance from `C` to `AB`
will be the perpendicular from `AB` through point `C`

This distance is
`color(white)("XXX")sin(30^@) * 18.6=1/2 * 18.6 =9.3`

Since this is the distance given as the length of `a` (`abs(CB)`)
There is only one possible solution.