Question

The triangle described is of the form SSA. Determine if there is no triangle possible, one trianglepossible, or two triangles possible. If only one triangle is possible, solve the triangle. If either twotriangles may be formed or no triangle may be formed, say so. The triangle is defined by:a = 10, c =8, y = 30'.Q=141.3", B = 8.7", b = 2.4No triangle can be formed from this information.a = 38.6,8 =111.41, b = 14.9Two triangles may be formed.

Answer 1

It is only possible to construct 1 triangle because the side non adjacent to angle y is greater than the adjacent side.

Now, we solve this triangle, for it we will use the cosines law:

$\begin{gathered} 10^2=b^2+8^2-2\cdot b\cdot8\cos (30)=b^2+64-2b\frac{\sqrt[]{3}}{2} \\ \text{solving for b} \\ b=14.9 \end{gathered}$

Using the law of sines we can obtein the remaining quantities. For this problem since is multiple choice we know the answer must be option number 3.