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

question 117

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 $a$ and $b$ are the lengths of two of the sides and $C$ is the included angle. If $A = 29$ in. $2 , a = 8$ in., $b = 9$ in., and $C$ is an acute angle, what must $C$ be? Give your answer in degrees to the nearest hundredth.

• A) \(26.83 ^ { \circ }\)
• B) \(53.66 ^ { \circ }\)
• C) \(126.34 ^ { \circ }\)
• D) No such triangle exists.

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