Solve the Problem $$\mathrm { A } = \frac { 1 } { 2 } \mathrm { ab } \sin \mathrm { C } \text {, }$$

question 206

Multiple Choice

Solve the problem.
-The area of a triangle is given by
$$\mathrm { A } = \frac { 1 } { 2 } \mathrm { ab } \sin \mathrm { C } \text {, }$$
where $\mathrm { a }$ and $\mathrm { b }$ are the lengths of two of the sides and $\mathrm { C }$ is the included angle. If $\mathrm { A } = 15$ in. 2 , $\mathrm { a } = 5$ in., $\mathrm { b } = 8$ in., and $\mathrm { C }$ is an acute angle, what must $\mathrm { C }$ be? Give your answer in degrees to the nearest hundredth.

• A) \(24.30 ^ { \circ }\)
• B) \(131.41 ^ { \circ }\)
• C) \(48.59 ^ { \circ }\)
• D) No such triangle exists.

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Pertaining to staphylococcus, a genus of gram-positive bacteria responsible for a variety of diseases and infections due to their toxin production.

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Referring to bacteria of the genus Streptococcus, which can cause various infections, ranging from mild sore throats to life-threatening diseases.