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.

---

Definitions:

Topic Expertise

Knowledge and skills in a particular area or subject.

Audience Participation

The involvement of spectators or listeners in the activity or performance they are witnessing.

Oral Presentation

A spoken report or speech given to an audience, often in a formal setting, for the purpose of sharing information, research, or ideas.

Visuals

Images, diagrams, charts, or any graphic elements used to support or enhance communication of ideas or data.