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3 years ago

Find the angle between a diagonal of a cube and a diagonal of one of its faces.

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

5 0

Answer:

35.26°

Step-by-step explanation:

If a cube has side length x

diagonal of the face = x×√2

The diagonal of the cube = x × √3

the angle between them is an acute angle in a right triangle,

opposite = x , adjacent = x×√2 , hyp. = x×√3

sin(angle) = x / ( x×√3 )

angle = sin^(-1) ( 1/√3) = 35.26

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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 23 feet up. The

leva [86]

The length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.

The ladder forms a right triangle as it lies against the wall as shown in the image below.

Thus:

x = length of the ladder (hypothenuse)

Reference angle $(\theta) = 75^{\circ}$

25 ft = Opposite

Apply SOH:

Thus,

$sin(\theta) = \frac{Opposite}{Hypotenuse}$

Plug in the values

$sin(75) = \frac{25}{x}\\\\x = \frac{25}{sin(75)} \\\\\mathbf{x = 25.88}$

Therefore, the length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.

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3 years ago

Find the number if 6% of it is 20% of 6

Anni [7]

Lets say 'x' is the number.

so you do 6/100 times x= 20/100 times 6
and that equals 6/100x=6/5
x=20
good luck!

4 0

3 years ago

Read 2 more answers

The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based o

Lina20 [59]

The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607

<h3>How to determine the regression equation?</h3>

The table of values is given as:

Completion Percentage 57 59 62 63 64

Interception Percentage 5 3.5 3 2.5 1.5

Next, we enter the above values in a graphing calculator.

From the graphing calculator, we have the following summary:

Sum of X = 305
Sum of Y = 15.5
Mean X = 61
Mean Y = 3.1
Sum of squares (SSX) = 34
Sum of products (SP) = -14.5
r = -0.9607

Regression Equation = ŷ = bX + a

b = SP/SSX = -14.5/34 = -0.42647

a = MY - bMX = 3.1 - (-0.43*61) = 29.11471

So, the regression equation is

y = -0.42647x + 29.11471

And the correlation coefficient is -0.9607