Answer :

Final answer:

To find the area of a triangle given two sides and the included angle, apply the formula Area = 0.5 * a * b * sin(C) and substitute the given values.

Explanation:

In this case, we're not dealing with a right triangle, so we can't apply the Pythagorean theorem directly. Instead, we need to apply the formula for the area of a triangle when given two sides and the included angle. This formula is given by: Area = 0.5 * a * b * sin(C), where a and b are the lengths of two sides, and C is the angle included between those two sides.

Substituting the given values into the formula, we find:

Area = 0.5 * 46.4 ft * 37.9 ft * sin(132.2°)

Computing this using a calculator (make sure it's in degree mode for the sine function), we find the Area of the triangle. Remember to round to an appropriate number of decimal places as needed in accordance with your teacher's or textbook's instructions.

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