Two opposite sides of a parallelogram have lengths of #3 #. If one corner of the parallelogram has an angle of #pi/12 # and the parallelogram's area is #14 #, how long are the other two sides?
1 Answer
Assuming a bit of basic Trigonometry...
Explanation:
Let x be the (common) length of each unknown side.
If b = 3 is the measure of the base of the parallelogram, let h be its vertical height.
The area of the parallelogram is
Since b is known, we have
From basic Trig,
We may find the exact value of the sine by using either a half-angle or difference formula.
So...
Substitute the value of h:
Divide by the expression in parentheses:
If we require that the answer be rationalized:
NOTE: If you have the formula