Two Sides and an Angle Are Given $$\mathrm { a } = 7 , \quad \mathrm {~b} = 9 , \quad \beta = 49 ^ { \circ }$$

question 102

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.
- $$\mathrm { a } = 7 , \quad \mathrm {~b} = 9 , \quad \beta = 49 ^ { \circ }$$

• A) two triangles
• \[\begin{array} { l }
• \alpha _ { 1 } = 76.01 ^ { \circ } , \gamma _ { 1 } = 54.99 ^ { \circ } , \mathrm { c } _ { 1 } = 7.60 \text { or } \\
• \alpha _ { 2 } = 103.99 ^ { \circ } , \gamma _ { 2 } = 27.01 , \mathrm { c } _ { 2 } = 12.14
• \end{array}\]
• B) one triangle
• \[\alpha = 35.94 ^ { \circ } , \gamma = 95.06 ^ { \circ } , \mathrm { c } = 11.88\]
• C) one triangle
• \[\alpha = 76.01 ^ { \circ } , \gamma = 54.99 ^ { \circ } , \mathrm { c } = 7.60\]
• D) no triangle

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