Solve the Equation for Solutions Over the Interval [0 $[ 0,2 \pi )$

question 144

Multiple Choice

Solve the equation for solutions over the interval [0, $[ 0,2 \pi )$ ) . Write solutions as exact values or to four decimal places, as
appropriate.
-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 $\mathrm { A } = 28$ in. $2 , \mathrm { a } = 9 \mathrm { in }$ ., $\mathrm { b } = 8 \mathrm { in }$ ., and $\mathrm { C }$ is an acute angle, what must $\mathrm { C }$ be? Give your answer in degrees to the nearest hundredth.

• A) \(128.94 ^ { \circ }\)
• B) \(51.06 ^ { \circ }\)
• C) \(25.53 ^ { \circ }\)
• D) No such triangle exists.

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