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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Related Questions
Classify the following triangle. Check all that apply. A. Scalene B. Right C. Acute D. Equilateral E. Obtuse F. Isosceles
Answers
Answer:
E and F
Step-by-step explanation:
The triangle given has two equal sides, and an obtuse angle that is more than 90° that measures 120°. The other two angles are of equal measure since their opposite sides are of the same length. Thus, this implies that it is an isosceles triangle because it has two equal base angles and two equal sides. It also implies that it is an obtuse triangle since one of it's angles is more than 90°.
Answer:
the correct answer is acute and scalene
At a real estate agency, an agent sold a house for $311,000. The commission rate is 4.6% for the real
ostate agency and the commission rate for the agent is 25% of the amount the real estate agency
goto How much did the agency make on the hous? How much did the agent cam in commission?
Answers
9514 1404 393
Answer:
agency: $14,306agent: $3,576.50Step-by-step explanation:
The agency's commission was ...
0.046 × $311,000 = $14,306
The agent's commission was ...
0.25 × $14,306 = $3,576.50
__
The agency made $14,306; the agent earned $3,576.50.
Pls help me ASAP I will give brainliest
Answers
Answer:
[tex]y = 40000(1.02)^8[/tex]
Step-by-step explanation:
Given
[tex]a = 40000[/tex] -- Initial population
[tex]r = 2\%[/tex] --- Rate
Required
Determine the population in 8 years
The question shows an exponential distribution and the final population will be calculated using:
[tex]y = a(1 + r)^x[/tex]
Where x is the number of years.
So, we have:
[tex]y = 40000(1 + 2\%)^8[/tex]
Convert % to decimal
[tex]y = 40000(1 + 0.02)^8[/tex]
[tex]y = 40000(1.02)^8[/tex]
(b) is correct
29 mm
가
120 mm
D
What is the perimeter?
millimeters
Answers
20^2 + b^2 = 29^2
400 + b^2 = 841
841 - 400 = 441
Square root 441 = 21
PERIMETER :
21+29+20 = 70
The answer is 70
Rodrigo acelera su bicicleta a razón de 0.9m/s2 bajo la acción de una fuerza de 94N ¿Cuál es la masa de ambos?
Answers
Answer:
no entiendo español
Step-by-step explanation:
no entiendo español
What is the slope of the line below?
(5,5)
(5,-2)
A. zero
B. negative
C. undefined
D. positive
Answers
Answer:
Undefined
Step-by-step explanation:
Vertical lines cannot be functions, since they yield multiple y-values for one single x-value.
The amount of miles a car travels and the gas remaining in the gas tank
A. Positive association
B. Negative association
C. No association
Answers
Answer:
B. Negative association
Step-by-step explanation:
As the car travels more miles, the gas in the tank will decrease.
what is 5.3 x 5.3 x 5.3 x5.3 as a power?
Answers
The expression 5.3 x 5.3 x 5.3 x 5.3 can be written as 5.3 raised to the exponentiation and powers of 4, or [tex]{(5.3)}^4[/tex], which evaluates to 6241.03.which means
To express this expression as a power, we need to determine the exponent that represents the number of times 5.3 is multiplied by itself. In this case, 5.3 appears four times in the multiplication.
So, the expression can be rewritten as 5.3 raised to the power of 4, or [tex]{(5.3)}^4[/tex].
The formula for expressing a number multiplied by itself n times as a power is: [tex]a^n[/tex]
In this case, a is 5.3 and n is 4.
To evaluate the expression, we can simply multiply 5.3 by itself four times:
5.3 x 5.3 x 5.3 x 5.3 = 6241.03
Therefore, 5.3 x 5.3 x 5.3 x 5.3 can be expressed as [tex]{(5.3)}^4[/tex], which is equal to 6241.03.
In summary, the expression 5.3 x 5.3 x 5.3 x 5.3 can be written as 5.3 raised to the exponentiation and powers of 4, or [tex]{(5.3)}^4[/tex], which evaluates to 6241.03.
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1 What is the value of this expression?
2 +4² x 4 - 12
Answers
Tell Me If Somethings wrong with my answer!
Answer:
54
Step-by-step explanation:
pedmas rule
2+16*4-12
2+64-12
66-12=54
. Suppose that 10 students of a class of 50 undergraduates are chosen for a behavioral experiment. The total class consists of 15 freshmen, 18 sophomores, 10 juniors, and 7 seniors. If all students are equally likely to be picked, determine the probability of the group contains exactly seven seniors and three juniors.
Answers
Answer:
Approximately 0% probability of the group contains exactly seven seniors and three juniors.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the students are chosen is not important, which means that we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
7 seniors, from a set of 7.
3 juniors, from a set of 10. So
[tex]D = C_{7,7} \times C_{10,3} = \frac{7!}{7!(7-7)!} \times \frac{10!}{3!(10-3)&} = 1 \times 120 = 120[/tex]
Total outcomes:
10 students froms a set of 50. so
[tex]T = C_{50,10} = \frac{50!}{10!(50-10)!} = 10272278170[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{120}{10272278170} \approx 0[/tex]
Approximately 0% probability of the group contains exactly seven seniors and three juniors.
35=7x. please help me fasttt
Answers
Answer:
x=5
Step-by-step explanation:
35 divided by 7 is 5, so in that case, 7 times 5 is 35.
What is the distance from Mto N?
4
N(2,3)
3
2
1
5 4 3 2
1
1 2
3 4 5
2
-3
4
M-4.-5)
A. 14 units
B. 100 units
C. 10 units
D. 2 units
Answers
9514 1404 393
Answer:
C. 10 units
Step-by-step explanation:
The distance MN can be found using the distance formula.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((2 -(-4))² +(3 -(-5))²) = √(6² +8²) = √100 = 10
The distance from M to N is 10 units.
There
are five marbles in
a bag. Three are green and
two are yellow. You draw a
marble, replace it, and then
Draw another. What is the
probability of choosing two
yellow marbles?
Answers
Answer:
like 20 percent
How many strikeouts per inning if there were 36 strikeouts in 60 innings
Answers
Answer:
0.6 strikeouts per inning
Step-by-step explanation:
36 strikeouts in 60 innings = 36/60 = 6/10 = 0.6
Answer: 0.6 strikeouts per inning
What is the measure of the missing angle
in the triangle below?
38
A 58°
B 52°
C 48°
D 42°
Answers
Answer:
B. 52°
Step-by-step explanation:
x + 38 + 90 = 180
x + 128 = 180
x = 180 - 128
x = 52°
I just need a little help
Answers
A right triangle and some of its measurements are shown in this diagram. Based on the measurements shown in the diagram, what is the value of T? HELP HELP GOD IMMA FAIL PLZ THIS IS URGENT
Answers
Answer:
t = 6√3 mm
Step-by-step explanation:
The angles of the triangle are 30°, 60°, and 90°. That's lucky for you, because the sides of a 30°-60°-90° triangle are always in the ratio 1:√3:2
The side opposite the 90° angle is 12 mm, so the side opposite the 30° angle is 12/2 = 6 mm
t = side opposite the 60° angle = 6√3 mm.
The value of T is 6√3.
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
We have,
Hypotenuse = 12 mm
Using Trigonometry
sin 60 = P/H
√3/2= P/12
12√3/2= P
P= 6√3
Thus, the value of T is 6√3.
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Answer:
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Answers
Answer:
$9.75
Step-by-step explanation:
This problem requires division. All factors are already provided in the problem, so all you have to do to solve this is divide 204.75/21, and get your answer! Hope this helps :)
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Answer:
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Step-by-step explanation:
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Find the simple interest you are investing $200 with a 5.2% interest rate of 3 years
Answers
Answer:
Step-by-step explanation:
Simple interest is
I=Prt, where I= interest, P=principle (initial value), r=interest rate, t=time
I=200(0.052)3
I=$31.20
Answer:
3,120
Step-by-step explanation:
Simple Interest= PRT / 100
= 200*5.2*3
= 1,040*3
= 3,120
Hope it is useful
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Answer: Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming or all of the US states in alphabetical order
What is 5% of 40? Need help please.
Answers
Answer:
it is 2
Step-by-step explanation:
set up and solve a quadratic equation to work out the value of x
Answers
Please help ! 1. Kenken puzzle 3x3
Answers
Answer:
Step-by-step explanation:
Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make the greatest number of bags that have all three cookie flavors and the same number of each flavor per bag. How many bags can he make without having any cookies left over? How many vanilla cookies will be in each bag?
Answers
Answer:
48 bags max if all 3 flavors must be in the bag. One flavor each in the bag.
I don't understand the other questions since the number of cookies per is not given nor the flavor mix
118.4 divided by 6.4 STEP BY STEP EXPLANATION PLS.
Answers
Answer: 18.5
Step-by-step explanation: Steps are down.
1. Move the decimal point all the way to the right.
2. Put a decimal point in the quotient exactly as the one in the dividend.
3. Divide the tens column by the divisor.
4. Multiply the divisor by the quotient.
5. Subtract the product by the divisor.
6. Bring down what's left, then repeat.
If AD = 21, BF = 8, and DF = 8, what is the value of AB?
Answers
Answer:
AB would be 21
Step-by-step explanation:
Sides BF and DF equal 8, because triangles BFC and DFC are both right triangles and they have two equal sides (hypotenuses are equal and both triangles share side FC), triangles BFC and DFC are congruent triangles, which means side DC is equal to BC. Since right triangles ADC and ABC share side AC and BC = DC, they are congruent triangles, meaning AB will equal AD, which is 21.
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Answer:
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Step-by-step explanation:
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3
Step-by-step explanation:
Answer:
9000
Step-by-step explanation:
