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

1 Answer
Nov 17, 2017

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.