Two Sides and an Angle Are Given $\mathrm { a } = 14 , \quad \mathrm {~b} = 12 , \quad \beta = 25 ^ { \circ }$

question 46

Multiple Choice

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s) that results.
- $\mathrm { a } = 14 , \quad \mathrm {~b} = 12 , \quad \beta = 25 ^ { \circ }$

• A) one triangle
• \[\alpha = 150.46 ^ { \circ } , \gamma = 4.54 ^ { \circ } , \mathrm { c } = 2.25\]
• B) one triangle
• \[\alpha = 29.54 ^ { \circ } , \gamma = 125.46 ^ { \circ } , \mathrm { c } = 23.13\]
• C) two triangles
• \[\begin{array} { l }
• \alpha _ { 1 } = 29.54 ^ { \circ } , \gamma _ { 1 } = 125.46 ^ { \circ } , \mathrm { c } _ { 1 } = 23.13 \text { or } \\
• \alpha _ { 2 } = 150.46 ^ { \circ } , \gamma _ { 2 } = 4.54 ^ { \circ } , \mathrm { c } _ { 2 } = 2.25
• \end{array}\]
• D) no triangle

Determine the most stable conformations of cycloalkanes and recognize the absence or presence of angle strain.

Identify the lowest energy conformations of cycloalkanes, including cyclobutane and cyclohexane configurations.

Analyze the factors contributing to the stability of chair and boat conformations of cyclohexane.

Apply knowledge of conformational analysis to name organic compounds accurately.

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