Question

How many triangles are possible given m∠A = 29°, c = 18, a = 17?

Answer 1

Two possible triangles exist.

Explanation:

Using a reference to the Law of Sines Ambiguous Case , we observe that `mangleA <90^@` and `a < c`, therefore, we must determine the height of the triangle:

`h = csin(A)`

`h ~~ 8.7`

This is the case where `h < a < c to 8.7 < 17 < 18`; two possible triangles exist.

Here is a drawing of the two possible triangles:

![www.desmos.com/calculator]()

The first triangle is the, red line, blue line and the x axis.

The second triangle is the red line, green line and the x axis.