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The area of a parallelogram is 456 , and the lengths of its sides are 25 and 62. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. Answer:

The area of a parallelogram is 456456 , and the lengths of its sides are 2525 and 6262. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.\newlineAnswer:

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Q. The area of a parallelogram is 456456 , and the lengths of its sides are 2525 and 6262. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.\newlineAnswer:
  1. Area Formula: The area of a parallelogram is given by the formula:\newlineArea=base×height \text{Area} = \text{base} \times \text{height} \newlineWe are given the area (456456) and the lengths of the sides (2525 and 6262). We can assume one of the sides to be the base. Let's choose the side with length 2525 as the base.
  2. Find Height: Now we need to find the height of the parallelogram. The height is the perpendicular distance from the base to the opposite side. Using the area formula, we can solve for the height (h):\newline456=25×h 456 = 25 \times h \newlineh=45625 h = \frac{456}{25} \newlineh=18.24 h = 18.24
  3. Calculate Angle: The height forms a right triangle with the base and the side of the parallelogram. The acute angle (let's call it θ) is the angle between the base and the side of length 6262. We can use the sine function to find this angle since we know the opposite side (height) and the hypotenuse (side of length 6262):\newlinesin⁡(θ)=oppositehypotenuse \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \newlinesin⁡(θ)=18.2462 \sin(\theta) = \frac{18.24}{62} \newlinesin⁡(θ)=0.294193548 \sin(\theta) = 0.294193548
  4. Find Angle: To find the angle θ, we take the inverse sine (arcsin) of the value we calculated:\newlineθ=arcsin⁡(0.294193548) \theta = \arcsin(0.294193548) \newlineUsing a calculator, we find that:\newlineθ≈17.1∘ \theta \approx 17.1^\circ

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