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.

---

Definitions:

Matched-Pairs Sample

An experimental design technique in which subjects are paired based on certain criteria, and each pair is treated differently to compare the effects.

Frequency Distributions

A summary of data showing the number (or frequency) of observations in each category of a variable.

Population Median

The population median is the value that divides the population into two equal halves, with half of the population values being less than the median and the other half being greater.

Population Mean

The average of a set of values in the entire population.