In Exercises 6 and 7, find sin J, sin K, cos J, cos K, tan J and tan K. Write each answer as a fraction and as a decimal rounded
to four places.
2 answers:
Answer: Refer to the diagram below for the answers
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Explanation:
The rules I'm using are
- sin(angle) = opposite/hypotenuse
- cos(angle) = adjacent/hypotenuse
- tan(angle) = opposite/adjacent
The opposite side is the leg furthest from the reference angle. For example, if J is the reference angle, then leg LK is the opposite side. The adjacent side would be JL for reference angle J. The opposite and adjacent swap when you swap the reference angle.
The hypotenuse is always the longest side and always opposite the largest angle (always opposite the 90 degree angle).
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An example calculation would be:
sin(angle) = opposite/hypotenuse
sin(J) = LK/JL
sin(J) = 30/34
sin(J) = 0.8824
I'm referring to the triangle with sides 16,30,34. The other trig ratios are handled in pretty much the same way (use the rules mentioned above).
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Step-by-step explanation:
Let's call A the amount of first type of fruit drinks. 55% pure fruit juice
Let's call B the amount of second type of fruit drinks. 80% pure fruit juice
The resulting mixture should have 65% pure fruit juice and 80 pints.
Then we know that the total amount of mixture will be:
Then the total amount of pure fruit juice in the mixture will be:
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:
+
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We substitute the value of A into one of the two equations and solve for B.