The area of a parallelogram is 13 , and the lengths of its sides are 3.6 and 5.6 . Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. Answer:

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Area Formula: The area of a parallelogram is given by the formula A = base * height, where the base is the length of one side and the height is the perpendicular distance from the base to the opposite side. We can use this formula to find the height of the parallelogram.Base and Height: Let's denote the base as b = 3.6 (without loss of generality, we can choose either side as the base) and the height as h. The area A is given as 13. So we have the equation 3.6 * h = 13.Calculate Height: Solving for h, we get h = 13 / 3.6. Calculating this gives us h ≈ 3.6111.Find Angle: Now, we need to find the acute angle θ between the base and the side of length 5.6. We can use the relationship between the side lengths and the height in a parallelogram, which involves the sine function: sin(θ) = opposite/hypotenuse = height/side_length.Sine Function: Substituting the known values into the sine function, we get sin(θ) = 3.6111 / 5.6.Calculate Sine Value: Calculating the sine value gives us sin(θ) ≈ 0.6452.Inverse Sine: To find the angle θ, we take the inverse sine (arcsin) of the sine value: θ = arcsin(0.6452).Final Angle: Calculating the inverse sine gives us θ ≈ 40.2°. Since this is an acute angle, it is the measure we are looking for.

The area of a parallelogram is $13$ , and the lengths of its sides are $3$ . $6$ and $5$ . $6$ . Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. $\newline$ Answer:

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The area of a parallelogram is $13$ , and the lengths of its sides are $3$ . $6$ and $5$ . $6$ . Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. $\newline$ Answer: