SOLUTION: Two sides of a parallelogram are 570 feet and 410 feet. The measure of the angle between these sides is 166 degrees. Find the area of the parallelogram to the nearest square foot.

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Question 935359: Two sides of a parallelogram are 570 feet and 410 feet. The measure of the angle between these sides is 166 degrees. Find the area of the parallelogram to the nearest square foot.
Found 2 solutions by Edwin McCravy, TimothyLamb:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Two sides of a parallelogram are 570 feet and 410 feet. The measure of the angle between these sides is 166 degrees. Find the area of the parallelogram to the nearest square foot.


The given angle (upper left) is 166° and since two 
adjacent angles of any parallelogram are supplementary
the angle at the lower left is 180°-166° = 14°

To find the area of the parallelogram, we need to find
it's height.  So we draw in the green line for the height
and label it h:



Then 





Put a 1 under the sine



Cross-multiply:



 feet.

Area of the parallelogram = base × height

                          = 570 ft × 99.1879772 ft.

                          = 56537.147 square feet

                          = 56537 square feet to the nearest square foot.

Edwin
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
adjacent angles of a parallelogram are supplementary:
---
H = 180 - 166
H = 14
---
find the height (h) of the parallelogram:
---
angle of the height with the base:
A = 90
---
using the law of sines:
a/sinA = h/sinH
410/sin(90) = h/sin(14)
h = sin(14)*410/sin(90)
h = 99.1879771959
---
area = bh
area = 570*99.1879771959
area = 56,537 sq.ft.
---
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