Question

How many solutions does a triangle with side lengths a = 4, A = 112°, and b = 9 have?

Use a numeral for your answer.

Answer 1

I'd say none. We can say:
\(\angle B + \angle C = 180^\circ - \angle A = 180^\circ - 112^\circ = 68^\circ\)
Which means that \(\angle B\) and \(\angle C\) are smaller than \(68^\circ\) and therefore also smaller than \(112^\circ\).
That makes \( \angle A \) is the biggest angle in the triangle and means that the side in front of it, which is \(a\), has to be the biggest side of the triangle.
But we are told that \(b = 9\) and \(a = 4\) which means \(b > a\) and therefore such a triangle cannot exist.

Answer 2

@pitamar thank you for helping me. What should I put as my answer it says use a numeral for your answer?

Answer 3

0?