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

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