Use the following identities:

Also because the angle is in quadrant 3, sin must be negative.
Therefore

Subbing in tan = 0.958
-1/4 + f/8 = 1/2.
The LCD is 8. Rewrite this equation as -8/4 + 8f/8 = 8(1/2) and then reduce the result:
-2 + f = =4
Then f = 6.
You should check this result.
We know that 20% of the first type of juice is pure fruit juice and 45% of second type of juice is pure fruit juice.
Now we have to make 30 pints of a mixture that is 35% pure.
Let x be the number of pints of first type of juice and y be the number of pints of second type of juice.
So,
(Equation 1)
Since, 20% of x + 45% of y = 35.3% of 30
(Equation 2)
Solving equations 1 and 2,
we get y=18 and x=12.
So, 12 pints of first type of juice and 18 pints of second type of juice are used.
P-6 because you subtract the variable from the 6