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Answer :
To find the area of triangle ABC, we can use the formula:
Area = (1/2) * a * b * sin(C)
Given that C = 133.9°, a = 45.9 ft, and b = 35.9 ft, we can substitute these values into the formula to calculate the area:
Area = (1/2) * 45.9 ft * 35.9 ft * sin(133.9°)
Using a calculator, we can evaluate sin(133.9°) to be approximately -0.923.
Area = (1/2) * 45.9 ft * 35.9 ft * (-0.923)
Calculating the expression on the right-hand side:
Area = 0.5 * 45.9 ft * 35.9 ft * (-0.923)
≈ -737.547 ft²
The area of triangle ABC is approximately -737.547 square feet.
It's worth noting that the negative sign indicates that the area is oriented in the opposite direction or is upside down. In practice, we consider the magnitude of the area, which is 737.547 square feet.
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