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To find the area of a triangle given the lengths of two sides and the angle between them, you can use the formula:
Area = 1/2 * a * b * sin(C)

where a and b are the lengths of the two sides and C is the angle between them in radians.

In this case, a = 7 inches, b = 4 inches, and the angle between them is 144 degrees.

First, convert the angle to radians:

144 degrees * (π / 180) = 2.51327 radians

Now, plug the values into the formula:

Area = 1/2 * 7 * 4 * sin(2.51327)
Area ≈ 8.2 square inches

Therefore, the area of the triangle is approximately 8.2 square inches.

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To determine the area of a triangle when given the measurements of two sides and the angle between them, one can utilize the formula: Area = 1/2 * a * b * sin(C), where a and b represent the lengths of the sides and C denotes the angle in radians.

For example, if a = 7 inches, b = 4 inches, and the angle between them is 144 degrees, the angle must first be converted to radians by multiplying it by (π / 180) to get 2.51327 radians.

Substituting these values into the formula, the area can be calculated as: Area = 1/2 * 7 * 4 * sin(2.51327), yielding an approximate area of 8.2 square inches.

Therefore, the area of the triangle would be approximately 8.2 square inches.