1. **Stating the problem:** Construct a triangle where one angle $m$ is less than 45 degrees, another angle $m$ is less than 90 degrees, and one side length is 3.6 cm. 2. **Understanding the problem:** We need to construct a triangle with two angle constraints and one side length given. 3. **Key rules:** - The sum of angles in any triangle is always $180^\circ$. - If one angle is less than $45^\circ$ and another is less than $90^\circ$, the third angle is $180^\circ$ minus the sum of these two. 4. **Step-by-step construction:** - Let angle $A < 45^\circ$ and angle $B < 90^\circ$. - Choose specific values satisfying these constraints, for example, $A = 40^\circ$ and $B = 80^\circ$. - Calculate angle $C = 180^\circ - (A + B) = 180^\circ - (40^\circ + 80^\circ) = 60^\circ$. 5. **Using the Law of Sines to find other sides:** - Given side $a = 3.6$ cm opposite angle $A$. - Law of Sines: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. - Calculate $b = \frac{a \sin B}{\sin A} = \frac{3.6 \times \sin 80^\circ}{\sin 40^\circ} \approx \frac{3.6 \times 0.9848}{0.6428} \approx 5.52$ cm. - Calculate $c = \frac{a \sin C}{\sin A} = \frac{3.6 \times \sin 60^\circ}{\sin 40^\circ} \approx \frac{3.6 \times 0.8660}{0.6428} \approx 4.85$ cm. 6. **Summary:** - Triangle with angles $40^\circ$, $80^\circ$, $60^\circ$ and sides approximately $3.6$ cm, $5.52$ cm, and $4.85$ cm. This satisfies the conditions $m < 45^\circ$, $m < 90^\circ$, and side length 3.6 cm.