The area of a parallelogram is 114cm³ if the adjacent sides are 12cm and 11cm calculate to the nearest degree the angle between them
To find the angle between the two adjacent sides of the parallelogram, we can use the formula:
Area = a * b * sin(theta)
where a and b are the lengths of the adjacent sides and theta is the angle between them.
Given that the area is 114 cm^2, side a is 12 cm, and side b is 11 cm, we can rearrange the formula to solve for theta:
114 = 12 * 11 * sin(theta)
114 = 132 * sin(theta)
sin(theta) = 114 / 132
sin(theta) = 0.8636
Now, we need to find the angle whose sin is 0.8636. Taking the arcsine of 0.8636 will give us the angle in radians, and then we can convert it to degrees.
Let's calculate:
theta = arcsin(0.8636)
theta ≈ 60.119 degrees
Therefore, the angle between the two adjacent sides of the parallelogram is approximately 60 degrees.