The adjacent sides of a parallelogram are 12cm and ycm. If the area is 84cm² and the angle between them is 150⁰ calculate the value of y
Given that the area of the parallelogram is 84 cm² and the adjacent sides are 12 cm and y cm. Let's call the angle between the two sides θ (150⁰).
The formula to calculate the area of a parallelogram is:
Area = base * height
In this case, the base is 12 cm and the height is y cm. We can express the height in terms of y and the angle θ using trigonometry. The height of the parallelogram is given by:
height = y * sin(θ)
Given that the area is 84 cm², we can write:
84 = 12 * y * sin(150⁰)
Using the sine of 150⁰:
sin(150⁰) = sin(180⁰ - 30⁰) = sin(30⁰) = 1/2
Substitute sin(150⁰) = 1/2 into the equation above:
84 = 12 * y * 1/2
84 = 6y
y = 84 / 6
y = 14
Therefore, the value of y is 14 cm.