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

question 71

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

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

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Definitions:

Normally Distributed

A statistical distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Normal Curve

A symmetrical bell-shaped curve that represents the distribution of a set of data, where most occurrences take place around the mean.

Asymptotic

The quality of the normal curve such that the tails never touch the horizontal axis.