Question

The area of a parallelogram is 7, and the lengths of its sides are 1.3 and 7.4. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.

Answer 1

To find the measure of the acute angle of a parallelogram, subtract the measure of the obtuse angle from 180 degrees. In this case, the obtuse angle can be found using the Law of Cosines, and then the acute angle can be determined by subtracting the obtuse angle from 180 degrees.

Step-by-step explanation:

To find the measure of the acute angle of a parallelogram, we can use the property that opposite angles of a parallelogram are congruent. Since the opposite angles are congruent, we can find the measure of one acute angle by subtracting the measure of the obtuse angle from 180 degrees.

In this case, the obtuse angle is the supplement of the acute angle. We can find the measure of the obtuse angle using the Law of Cosines, which states that c^2 = a^2 + b^2 - 2ab*cos(C). Plugging in the values given, we get (7.4)^2 = (1.3)^2 + 7^2 - 2(1.3)(7)*cos(C). Solving for cos(C) gives us cos(C) = 0.9341, and taking the inverse cosine we find C to be approximately 20.7 degrees.

Since the acute angle and obtuse angle are supplementary, the measure of the acute angle is 180 - 20.7 = 159.3 degrees.