Find the measure of each angle indicated. Round to the nearest tenth.

Answer:

missing angle = 67.8 degrees

Step-by-step explanation:

[tex]cos-1 = \frac{adjacent}{hypotenuse}[/tex]

[tex]cos-1 = \frac{5.3}{14}[/tex]

[tex]cos-1 = 0.378571428[/tex]

[tex]67.754 = 67.8[/tex]

C) 67.8° is the value of theta in the given right-angled triangle.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, a right-angled triangle whose adjacent and hypotenuse are 5.3 and 14 respectively.

We know cos(theta) =  adjacent/hypotenuse.

∴ theta = cos⁻¹(adjacent/hypotenuse).

theta = cos⁻¹(5.3/14).

theta = cos⁻¹(0.3786).

theta = 67.8°.

learn more about inverse trigonometric functions here :

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Can someone please explain this to me?

A 8-foot ladder touches the side of a building at a point 6 feet above the ground. At what height would a 22-foot ladder touch the building if it makes the same angle with the ground as the shorter ladder? Round to the nearest tenth if necessary.

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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)




(Score for Question 3: ___ of 7 points)
3. You have been hired as a consultant by Mr. Robbins of the large Ice Cream company Dachshund Robbins. As part of assisting them with determining things like the number of cones that can be made per container of ice cream they’ve asked you to determine the amount of ice cream in a properly filled cone.

Mr. Robbins Ice cream cone reference
image with full scoop
Please note Mr. Robbins is very insistent that all cones be properly filled, and that he’s running an honest business.
Answer:
Find the volume of the composite shape for Mr. Robbins, and make sure to show your work)

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A
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