Two opposite sides of a parallelogram have lengths of #8 #. If one corner of the parallelogram has an angle of #pi/8 # and the parallelogram's area is #12 #, how long are the other two sides?
2 Answers
Nasty answer. Here's a walkthrough.
Explanation:
Let h be the (perpendicular) height extending from one of the bases that measures length b = 8 to the other base having the same length.
since A = bh = 8h is the area of the parallelogram, we have
8h = 12
Let c be the length of one of the unknown sides.
From basic trigonometry,
We may obtain the value of
That value is
So that...
Cross multiply:
If we demand that the expression be rationalized, then
multiply first by
Picture
Explanation:
If you also have the formula
where
Use the value of the sine, and it comes out quickly.