Question

Make up three problems involving oblique triangles. One should result in one triangle, the second in two triangles, and the third in no triangle.

Short answer

Problem 1. $c=5,b=3,C={60}^{\circ }$

Problem 2: $c=2,b=3,C={20}^{\circ }$

Problem 3:$c=2,b=3,C={20}^{\circ }$

Step-by-step solution

Step 1. Given Information

We have to write three problems involving oblique triangles. One should result in one triangle, the second in two triangles, and the third in no triangle.

Step 2. Problem 1

Problem 1: You are given two sides and an angle, determine whether these parameters form one, two, or no triangles:

$$\begin{gathered} c=5 \\ b=3 \\ C={60}^{\circ } \end{gathered}$$

(Results in one triangle)

Step 3. Problem 2

Problem 2: You are given two sides and an angle, determine whether these parameters form one, two, or no triangles:

$$\begin{gathered} c=2 \\ b=3 \\ C={20}^{\circ } \end{gathered}$$

(Results in two triangles)

Step 4. Problem 3

Problem 3: You are given two sides and an angle, determine whether these parameters form one, two, or no triangles:

$$\begin{gathered} c=2 \\ b=3 \\ C={60}^{\circ } \end{gathered}$$

(Results in no triangles)