Consider a square-based straight pyramid. Suppose that the base is a square with sides 10 km long, and all other edges are 17 km long. Find an approximate value of the angle formed between the base and a triangular face. Present your answer in degrees, accurate up to four or more decimal places.
Answers
Answer:
72.06
Step-by-step explanation:
Given that :
Side Lenght, a = 10
Edge length, b = 17
Using Pythagoras :
h = height of pyramid
h = sqrt (b² - 1/2a²)
h = sqrt(17^2 - 10^2/2)
h = sqrt(289 - 50)
h = 15.46
Slant height :
L = sqrt(h² + a²/4)
L = sqrt(15.46² + 25)
L = sqrt(239 + 25)
L = sqrt(264)
L = 16.25
Sinα = h/L
α = sin^-1 (15.46/16.25)
α = 72.060933
= 72.06
The approximate value of the angle formed between the base and a triangular face is 72.0775°.
Let [tex]h[/tex] be the distance between the center of the square base and the midpoint of the side of the square and let [tex]H[/tex] the height of the triangular face of the pyramid. By properties of the square and the Pythagorean theorem we derive expressions for [tex]h[/tex] and [tex]H[/tex], respectively:
Square base
[tex]h = 0.5\cdot L[/tex] (1)
Triangular face
[tex]H = \sqrt{l^{2}-0.25\cdot L^{2}}[/tex] (2)
Where:
[tex]L[/tex] - Side length of the square base, in kilometers.[tex]l[/tex] - Remaining side length of the triangular face, in kilometers.Finally, by trigonometry we can derive an expression for the angle between the base and a triangular face ([tex]\theta[/tex]), in sexagesimal degrees:
[tex]\theta = \cos^{-1} \frac{h}{H}[/tex] (3)
If we know that [tex]L = 10\,km[/tex] and [tex]l = 17\,km[/tex], then the angle between the base and a triangular face is:
[tex]h = 5\,km[/tex]
[tex]H = \sqrt{17^{2}-5^{2}}[/tex]
[tex]H \approx 16.248\,km[/tex]
[tex]\theta = \cos^{-1} \frac{5\,km}{16.248\,km}[/tex]
[tex]\theta \approx 72.0775^{\circ}[/tex]
The approximate value of the angle formed between the base and a triangular face is 72.0775°.
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Find the value of x so that the ratios are equivalent.
1:8 and 4:x
X =
Answers
Answer:
32
Step-by-step explanation:
1 : 8 = 4 : 32
So, 4 : x = 4 : 32
x = 32
The value of x from the given ratios is 32.
Given that, the ratios 1:8 and 4:x are equivalent.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here,
1:8 =1/8
4:x =4/x
Ratios are equivalent 1/8 = 4/x
x= 4×8
x=32
Therefore, the value of x from the given ratios is 32.
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What is the multiplicative inverse of the number 5?
Answers
Answer:
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Step-by-step explanation:
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Answers
Will give brainliest
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Step-by-step explanation:
$20 haircut; 10% tip Find the total cost
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Answers
Answer:
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Step-by-step explanation:
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7 cm
3 cm
Nor drawn
accurately
A square has the same perimeter as the rectangle.
What is the side length of this square?
Answers
Answer:
a square and rectangle have the same perimeter. the length of the rectangle is 4 cm less than twice the side of the square, and the width of the rectangle is 6 cm less than the side of the square.
Step-by-step explanation:
jayfeather friend me
The required side length of the square is 5 cm.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
Length of rectangle = 7 cm,
Width of rectangle = 3 cm.
The perimeter of rectangle = 2(length + width)
= 2(7 + 3)
= 2 x 10
= 20
Also, given that the perimeter of the rectangle is equal to the perimeter of a square,
Let side of square is a then perimeter = 4a
⇒ 4a = 20
⇒ a = 5
The side length of the square is 5 cm.
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What is the solution to the system of equations below?
x = 5y - 2 AND 3x - 4y = 27 *
Answers
Answer:
x = 13, y = 3
Step-by-step explanation:
3(5y - 2) - 4y = 27
15y - 6 - 4y = 27
11y = 33
y = 3
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∠AHD and ∠AHB
∠DHB and ∠BHF
∠AHD and ∠BHF
I don't know.
Imported Asset
Answers
Answer:
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Step-by-step explanation:
Because they share a common side
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Answer:
Step-by-step explanation:
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Simplify
6sqrt20 + 8sqrt5 - 5sqrt45
Answers
Answer:
20√5 - 10√10
Step-by-step explanation:
6√20 + 8√5 - 5√45
first, 6√20 and 5√45 need to be simplified. 8√5 cannot be simplified any further:
6√20 = 6√4•5 = 6√2•2•5 = 6•2√5 = 12√5
5√45 = 5√8•5 = 5√2•2•2•5 = 5•2√2•5 = 10√10
now:
12√5 + 8√5 - 10√10
then, add the coefficients of 12√5 and 8√5
20√5 - 10√10
the left over numbers cannot be combined because they do not have a common radical, making 20√5 - 10√10 the final answer
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Step-by-step explanation:
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Step-by-step explanation:
i’m doin this i-ready and got it right
At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram.
A tree diagram. Random student studies for test is 0.6, and does not study for test is 0.4. Studies for test to Gets B or higher is 0.55; does not get B or higher is 0.45. Does not study for test to Gets B or higher is 0.20; does not get B or higher is 0.80.
The professor informs the class that there will be a test next week. What is the probability that a randomly selected student passes the test with a B or higher?
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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g(x) = -x-1, -2≤x<1
g(x)=6, 1≤x≤3
We need to find value of g(0).
Let us check at which interval the value zero lies.
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Hence, the value of the function g(0) is -1.
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Can some one help me with these 2 questions I’ll give you brainliest
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Step-by-step explanation:
Multiply numerator and denominator by the conjugate of the denominator.
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the attachment is not clearly
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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g(a) = 3 - 2aStep-by-step explanation:
Given
As the function g(x) is given by
[tex]g(x)=3-2x[/tex]
To determine
g(a) = ?
In order to determine g(a),
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g(a) = 3 - 2ajtftfjjvvjvghchvjufvyffytrcf
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Answers
Answer:
The one on the top right
Step-by-step explanation:
It displays 8 steps each with a length of 1/2 to represent 8 x 1/2.
HTH :)
Mr. Saslow needs to buy a drink, chips and a sandwich for lunch. He has $15 to spend on his lunch. If
the total cost of the drinks and chips was 4 dollars, which inequality represents the dollar amount, d,
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d. d > 19
Answers
Answer:
a. d < 11
Step-by-step explanation:
4 + d < 15
d < 15 - 4
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What is the slope of the line below?
(5,5)
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Answers
Answer:
Undefined
Step-by-step explanation:
Vertical lines cannot be functions, since they yield multiple y-values for one single x-value.
The question is in the attachment
Answers
Answer:
120
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Step-by-step explanation:
120= 2x2x2x3x5
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Multiply all the common prime factors.
2x3x5
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WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
is they fhour the repondet
Answer:
B. 0! x 4 = 4
Step-by-step explanation:
0! is equal to 1 so
1 times 4 is 4
So the answer is
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Answer:
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Step-by-step explanation:
Hank cut his pizzainto 10 pieces and ate 6 of the pieces.Rose cut her pizza into 5 pieces and ate the same amount as hankShow this on a drawing
Answers
Answer:
well you would have to draw two pizzas or circles
Step-by-step explanation:
what you would to is draw lines to separate one of them into 10 peices and the other one into 5. You can shade in the 6 peices Hank ate and then shade the same amount of pizza on Roses. Hope this helped!