The area of a parallelogram is 2 , and the lengths of its sides are 2.1 and 1.4. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. Answer:

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Understand Formula: The area of a parallelogram is given by the formula A = base * height, where the height is the perpendicular distance from the base to the opposite side. In this case, we can consider one of the sides as the base and the other as the corresponding height, since we are looking for the acute angle between them.Identify Base and Height: Let's denote the side of length 2.1 as the base (b) and the side of length 1.4 as the height (h) for our initial calculation. The area (A) of the parallelogram is given as 2. Using the formula A = b * h, we have 2 = 2.1 * h.Calculate Height: Solving for h, we get h = 2 / 2.1. Calculating this, we find h = 0.95238095238.Check Validity: However, we must check if this height corresponds to the actual height when considering the side of length 2.1 as the base. The height we have calculated must be less than or equal to the length of the other side, which is 1.4, for it to be the correct height. Since 0.95238095238 is less than 1.4, our height is valid.Find Sine of Acute Angle: Now, we can find the sine of the acute angle (θ) using the formula sin(θ) = opposite / hypotenuse, where the opposite side is the height (h) and the hypotenuse is the side of length 1.4. So, sin(θ) = h / 1.4 = 0.95238095238 / 1.4.Calculate Acute Angle: Calculating the sine of the acute angle, we get sin(θ) = 0.68027210884.To find the measure of the acute angle, we take the inverse sine (arcsin) of the value we calculated. θ = arcsin(0.68027210884).Calculating the inverse sine, we get θ ≈ 43.3° to the nearest tenth of a degree.

The area of a parallelogram is $2$ , and the lengths of its sides are $2$ . $1$ and $1$ . $4$ . 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 $2$ , and the lengths of its sides are $2$ . $1$ and $1$ . $4$ . Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. $\newline$ Answer: