How many solutions does a triangle with side lengths a=4, a=68 degrees, and b=10 have?

2 possible solutions

Step-by-step explanation:

First we need to construct the three different triangles, shown in the image.

After we put the equations for each triangle:

Triangle 1:

Triangle 2:

Triangle 3:

As all are quadratic equations, so we resolve them with the general formula for quadratic equations, then we have 6 numerical solutions, but we can only consider those that are positive and real.

For triangle 1:

For triangle 2:

For triangle 3:

So, with the previous results, the only ones that are possible to construct a triangle are:

Triangle 1: because is positive

Triangle 2: because is positive

Triangle 3: None as both are imaginary

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)