Question

Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13.

Answer 1

General rule is a<bsinA means no triangle is possible, a=bsinA means 1 triangle is possible and a>bsinA means 2 possible triangles

Answer 2

To get the possible triangle that be formed with a triangle whose dimensions are C=85, a=10 and c=13, we need to calculate for the values of the angles. Using sine rule:
a/sin A=c/sin C=d/sin D
thus the value of angle A will be:
10/sin A=13/sin 85
10/sin A=13.05
sin A=10/13.05
sin A=0.7663
A=arcsin 0.7663
A=50
thus the n=value of angle B will be:
B=180-(85+50)
=45
The triangle formed will be an acute triangle