### Instruction: One angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. What is the area of the parallelogram? Express your answer in simplest radical form.### Response: I know that the area of a parallelogram is the base times the height, where the height is the perpendicular distance from the base to the opposite side.
I also know that opposite angles of a parallelogram are congruent, so the other angle opposite the 120-degree angle is also 120 degrees.
To find the height, I need to use some trigonometry.
I can draw a right triangle inside the parallelogram by dropping a perpendicular from one vertex to the opposite side.
This triangle has a hypotenuse of 15 inches and an acute angle of 60 degrees, since 180 - 120 = 60.
I can use the sine function to find the height, since sine is opposite over hypotenuse.
So, sin(60) = h / 15, where h is the height.
Multiplying both sides by 15, I get h = 15 sin(60).
I remember that sin(60) is the same as the square root of 3 over 2, so I can simplify h as 15 times the square root of 3 over 2.
Now that I have the height, I can find the area by multiplying it by the base, which is 8 inches.