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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Definitions:

Test Statistic

A calculated value from sample data used to decide whether to reject the null hypothesis in statistical hypothesis testing.

Significant Change

An alteration in data or a pattern that is considered to be of importance due to its impact or magnitude.

Goodness of Fit

A statistical test to see how well sample data fits a distribution from a population with a normal distribution.

Degrees of Freedom

The number of independent values or quantities that can variably assign to a statistical calculation without breaking any constraints.