find the values of x and y.

Answer:

x = 4[tex]\sqrt{6}[/tex] , y = 8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle on the left and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex]

let the altitude of the outer triangle be h ( common to both right triangles )

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{8}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2h = 8[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

h = 4[tex]\sqrt{2}[/tex]

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Using the tangent ratio in the right triangle on the right and the exact value

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{x}[/tex] = [tex]\frac{4\sqrt{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

x = 4[tex]\sqrt{6}[/tex]

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Using the sine ratio in the right triangle on the right and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{h}{y}[/tex] = [tex]\frac{4\sqrt{2} }{y}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

y =8[tex]\sqrt{2}[/tex]

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Graded Assignment
Unit Test, Part 2: Volume
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit.
Please make certain to show your work as part of your grade is associated with showing the steps to complete a problem. You want to set things up so that someone else can see the process you used to arrive at your answer.
Total score: ____ of 15 points
(Score for Question 1: ___ of 4 points)
1. Akari has a sink that is shaped like a half-sphere. The sink has a volume of
3. One day, her sink clogged. She has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely full when Akari begins scooping. Hint: you may need to find the volume for both.
(a) Cup A has a diameter of 4 in. and a height of 8 in. Find the Volume of Cup A.
(b) Determine how many cups of water must Akari scoop out of the sink with Cup A to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work.
(c) Cup B has a diameter of 8 in. and a height of 8 in. Find the volume of Cup B.
(d) How many cups of water must she scoop out of the sink with Cup B to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work. Answer:
Part A)

Part B)


Part C)

Part D)




(Score for Question 2: ___ of 4 points)
2. Asahi also has a sink that is shaped like a half-sphere. The sink has a volume of 3. One day, his sink clogged. He has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Asahi begins scooping. Hint: you may need to find the volume for both.
(a) Cup G has a diameter of 4 in. and a height of 8 in. Find the volume of Cup G.
(b) How many cups of water must Asahi scoop out of the sink with Cup G to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work.
(c) Cup H has a diameter of 8 in. and a height of 8 in. Find the volume of Cup H.
(d) How many cups of water must he scoop out of the sink with Cup H to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work. Answer:
Part A)

Part B)


Part C)

Part D)




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Mr. Robbins Ice cream cone reference
image with full scoop
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