Question 243871: find the area of a parallelogram with an angle of 65 degrees 16 minutes included between two sides of 19 and 23.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I will assume the horizontal side is 23 and the slanting side is 19.
This should work either way.
Area of a parallelogram is equal to base * height.
The base would be equal to 23.
The height is what you have to find.
The angle is 65 degrees 16 minutes which equates to an angle of 65 + 16/60 degrees which equals 65.2666666667 degrees.
Since the sine of this angle is equal to opposite / hypotenuse, and hypotenuse is equal to 19, and opposite equals height, then this formula becomes:
sine (angle) = height / 19 which makes:
height = 19 * sine (angle).
since the angle iss 65.26666666667 degrees, then this formula becomes:
height = 19 * sine (65.2666666667) which becomes:
height = 19 * .908264919 which becomes:
height = 17.25703345
this makes the area = to 17.25703345 * 23 = 396.9117694 square units.
assuminb the base was 19 and the slant was 23, then this formula becomes:
height = 23 * .908264919 which becomes:
height = 20.89009313
this makes the area = t 20.89009313 * 19 = 396.9117694 square units.
the area is the same as it should be.
your parallelogram would look something like this:
23 units
xxxxxxxxxxxxxxxxxxxxxxxxxxxx
x xx
x x x 19 units
x height --> x x
x x x <---65.267 degrees
xxxxxxxxxxxxxxxxxxxxxxxxxxxx
|
|
|
