Question

The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle possible, or two triangles possible. If only one triangle is possible, solve the triangle. If either two triangles may be formed or no triangle may be formed, say so. The triangle is defined by: a=4 b=6 A=60

Answer 1

Explanation:

First thing you have to do is set up the triangle with its angles and sides given. Since angle A and side a are given, I made the angle one of the base angles and the side then is across from it. I made angle B the other base angle since its side was also given. Use the values of angle A and side a to solve for the height of the triangle.

`sin60=(h)/(6)` and

6 sin 60 = h so

h = 5.196

The rules for 0 triangles is that angle A has to be acute (which it is) and side a has to be less than the height. If that is true, then no triangle exists here. Side a is 4 and the height is 5.196. Side a is less than h, so there is no triangle formed here. Side a is too short to close it up.