The area of a parallelogram is 60cm. If the two adjacent sides are 15cm and 6cm, respectively find the angle between them
The area is 15*6*sinθ = 60
so, ...
To find the angle between the two adjacent sides of a parallelogram, you can use the formula:
Angle = arccos((a^2 + b^2 - c^2) / (2 * a * b))
Given that the two adjacent sides of the parallelogram are 15cm and 6cm, respectively, let's label them as side a = 15cm and side b = 6cm.
We can use the given area of the parallelogram to find the length of the other two sides, which are also equal to each other.
The area of a parallelogram is given by the formula:
Area = base * height
Since the height of the parallelogram is perpendicular to the base, we can use the formula:
Area = base * height = a * h
By substituting the given area (60cm^2) and the first side (a = 15cm) into the formula, we can solve for the height (h):
60cm^2 = 15cm * h
h = 60cm^2 / 15cm
h = 4cm
Therefore, the height of the parallelogram is 4cm.
Now, we can use the Pythagorean theorem to find the remaining side length (c):
c^2 = a^2 - h^2
c^2 = 15cm^2 - 4cm^2
c^2 = 225cm^2 - 16cm^2
c^2 = 209cm^2
c ≈ 14.45cm
Now that we have all the side lengths, we can substitute them into the formula for finding the angle between adjacent sides:
Angle = arccos((a^2 + b^2 - c^2) / (2 * a * b))
Angle = arccos((15cm^2 + 6cm^2 - 14.45cm^2) / (2 * 15cm * 6cm))
Angle = arccos((225cm^2 + 36cm^2 - 209cm^2) / (180cm * cm))
Angle = arccos(52cm^2 / 1080cm^2)
Angle ≈ arccos(0.0481)
Angle ≈ 87.9 degrees (rounded to one decimal place)
Therefore, the angle between the two adjacent sides of the parallelogram is approximately 87.9 degrees.