Question

The area of a parallelogram is 37, and the lengths of its sides are 4.3 and 9.9. 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 the parallelogram, use the formula Area = base x height x sin(angle). Plug in the given values and solve for the angle using a calculator.

Step-by-step explanation:

To find the measure of the acute angle of the parallelogram, we can use the formula:

Area = base x height x sin(angle)

Given that the area is 37 and the lengths of the sides are 4.3 and 9.9, we can rearrange the formula:

37 = 4.3 x 9.9 x sin(angle)

Solving for sin(angle), we get:

sin(angle) = 37 / (4.3 x 9.9)

Using a calculator, we find that sin(angle) ≈ 0.841

Therefore, angle ≈ sin^(-1)(0.841)

≈ 58.2 degrees (rounded to the nearest tenth).