To determine the diameter of the sun, an astronomer might sight with a transit (a devise used by surveyors for measuring angles), first to one edge of the sun and then to the other, finding that the included angle equals 32 minutes (32'). Assuming that the distance from the Earth to the sun is 92,919,800 miles, calculate the diameter of the sun.

Answers

Answer 1

This will help explain it to you!

Answer 2

Final answer:

The astronomer calculates the diameter of the Sun using trigonometry and the given angle and distance, arriving at an approximate value of 1,727,804 miles which is a reasonable estimate when compared to the actual diameter of the Sun.

Explanation:

To calculate the diameter of the Sun, the astronomer uses the given angular size and the distance from the Earth to the Sun. Since we have the angle of 32 minutes (which is about 0.533° when converted to degrees), we can set up the following relationship using trigonometry:

diameter of the Sun = 2 × (distance to the Sun) × tan(½ × angular size in radians)

Let's convert the angular size from minutes to degrees and then to radians:

32 minutes = 32' / 60 = 0.533°

To convert degrees to radians, we use the fact that 180° is equivalent to π radians:

0.533° × (π radians / 180°) = 0.0093 radians

Now, we can use the distance to the Sun which is given as 92,919,800 miles and apply the formula:

diameter of the Sun = 2 × 92,919,800 miles × tan(0.0093 radians)

Performing the calculation:

diameter of the Sun ≈ 2 × 92,919,800 × 0.0093

diameter of the Sun ≈ 1,727,804 miles

This is an approximation because the angular size varies slightly due to the elliptical orbit of Earth. Comparing to the actual diameter of the Sun, which is about 1.39 million kilometers (or about 864,000 miles), we can see that our calculated value is a reasonable estimate, keeping in mind that trigonometric calculations rely on a circular orbit assumption and ideal conditions.

Related Questions

Macon is 50 miles from Atlanta. If the time of the trip increases, what happens to the speed?

Answers

The speed has slowed down.

it slows down hope this helps

What is 395 times blank equals 2,370

Answers

6

Oh no! Something went wrong while adding your answer
It's too short. Write at least 20 characters to explain it well.

first divide 2,370 and 395 which we will get 6.

Check:
395 x 6= 2,370

Please help asap! Number 2 , picture is included! (10 points)

Answers

So, first, we know that the whole angle must equal 90 because there's a right angle symbol, and right angles equal 90 degrees.

So, 43 + x + 3 must equal 90.

Or, 46 + x = 90

Then subtract 46 from both sides.

x = 90 - 46

x = 44

These would also be adjacent angles because they share the same vertex.

Danielle works as a cashier in a bookstore she works 35 hours a week and earns $11 an hour each week Daniella spends $300 answer saves the rest . Danielle estimates that she earns about $20000 per year is this estimate accurate? explain

Answers

Danielle's estimate of earning about $20,000 per year is accurate, as the calculation based on her hourly wage and weekly hours worked gives an actual annual income of $20,020.

Danielle's estimate of earning about $20,000 per year is accurate based on her hourly wage and weekly hours worked. To assess the accuracy of her estimate, we need to calculate her actual annual income.

Danielle earns $11 per hour and works 35 hours a week. Therefore, her weekly earnings are:

35 hours/week × $11/hour = $385/week.

As there are typically 52 weeks in a year, her estimated annual income would be:

52 weeks/year × $385/week = $20,020/year.

This calculation shows that Danielle's estimate of making about $20,000 per year is indeed accurate.

List factor pairs of 56

Answers

1 and 56, 2 and 28, 4 and 14, 7 and 8

Factor pairs are pairs of numbers that, when multiplied together, equal the original number. Prime numbers only have the factors 1 and the number itself.
I start by prime factoring the number, then combining our primes to make the factor pairs:
56 = 8 x 7
56 = 2 x 2 x 2 x 7

For 56, we have:
1 and 56
2 and 28 (2, then combine 2 x 2 x 7)
4 and 14 (2 x 2 = 4 , then combine 2 x 7=14)
7 and 8 (2 x 2 x 2=8, then 7)

If you like my answer, please give me a 'brainliest' - I'm trying to quickly improve my site ranking :-)

Morgan plots the point (4,-7) on a coordinate plane. If she reflects the point aacross the y axis, what are the coordinates of the reflected point?

Answers

(-4,-7)

The x coordinate just becomes a negative

If you imagine a coordinate plane, there are 4 sections.
1 : (+,+)
2 : (-,+)
3 : (-,-)
4: (+,-)

Now, point (4,-7) is in the 4th section. Meaning, the reflection over the y-axis would be in the 3rd section. It would be (-,-)

The reflection over the y-axis of (4,-7) is (-4,-7).

I hope this helps!

what is 235 written as a product of prime factors?

Answers

235/5 = 47

5 and 47 are prime, so

235 = 5 * 47

5 divides into 235 without a remainder; the quotient is 47. 47 is prime; it does not have integer factors other than 1 and 47.

Thus, 235 = 5(47) (answer: product of prime factors)

What is −412√+75√ in simplest radical form?

Answers

Ok
√12 = √4 * √3 = 2√3
√75 = √25*√3 = 5√3

so 4√12 + √75 = 4*2√3 + 5√3 = 13√3 answer

Answer: 13√3.

Step-by-step explanation: Given radical expression 4√12 + √75.

Let us simplify each of the radical separately first.

√12 = √(2×2×3) = 2√3

Therefore, 4√12 = 4 × 2√3 = 8√3.

√75 = √(3×5×5) = 5√3

Therefore 4√12 + √75 => 8√3 + 5√3.

Adding like radicals, we get

8√3 + 5√3 = 13√3.

Therefore, 4√12 + √75 = 13√3.

Explain whether or not you think the relationship is linear or not.

The pond in Tom’s backyard holds 50 gallons of water and recedes at a rate of 5 gallons per day.

Answers

It’s nonlinear because the 50 isn’t changing so if you made a graph of this problem (y=5x+50) it would not be a straight line.

the soccer field at Mario's school has an area of 6,000 square meters. how can mario show the area as a whole number multiplied by a power of 10?

Answers

6,000 = 6 x 10^3 square meters.
6,000 = 60 x 10^2 square meters
6,000 = 600 x 10^1 square meters.
You can pick which you wish to report in.
Hope this helps :-)

Answer: [tex]6\times10^3[/tex] square meters.

Step-by-step explanation:

Given : The soccer field at Mario's school has an area of 6,000 square meters.

Here, 6,000 can be written as [tex]6\times1,000[/tex]

And [tex]1000=10\times10\times10=10^3[/tex] [using exponents]

Then, 6,000 can be written in the form of a whole number multiplied by a power of 10 as [tex]6,000=6\times10^3[/tex]

Hence, Maria can show the area as [tex]6\times10^3[/tex] square meters. .

Convert: 2°C to °F (to the nearest tenth).

Answers

i feel like it is 35.6°

what is the range of 34, 56, 13, 98, 75

Answers

the range is the highest number minus the lowest number

98 - 13 = 85 <==

Answer:

Range = 85

Step-by-step explanation:

The formula for range of a data set is

Range = Maximum value - Minimum value

The given data set is

34, 56, 13, 98, 75

In this data set we have,

Maximum value = 98

Minimum value = 13

The range of given data set is

Range = 98 - 13

Range = 85

Therefore, the range of the data is 85.

a mathematical term that does not include an equal or inequality sign is called an

Answers

This is an expression.

Помогите пожалуйста

Answers

It is irrational because it cannot be written as a ration of two integers .

65 in. =__ft.

A. 6 5/12 ft.
B. 12 ft.
C. 5 5/12 ft.
D. 780 ft

Answers

there are 12 inches in one foot. divide 65 inches by 12 inches.

65/12= 5.416666667

as a fraction, this equals C, or 5/12.

Hope this helps and have a great day! :D

12+12+12+12+12=60+5in=65
1 2 3 4 5

C. 5 5/12

4y−2(3/2y−5) simplify

Answers

First you distribute:
4y - (2 * [tex] \frac{3}{2} [/tex]y) - (2 * 5)
4y - 3y - 10

Then you combine like terms:
(4y + -3y) - 10
1y - 10

Simplify:
y-10

The coordinates of the vertices of ΔXYZ are (4, –1), (2, –4),
and (7, –4).
The coordinates of image ΔXʹYʹZʹ are (−4, −1), (−2, −4), and (−7, −4).
This transformation can be expressed as (x, y) ⟶ (−x, y).

Is the orientation of ΔXYZ the same as the orientation of ΔXʹYʹZʹ?
Why or why not?

Answers

No because when you graph both triangles on a graph the points do not correspond to the same place. Hope this helps

zachary purchased a computer for 1800 on a payment plan. three months after he purchased the computer, his balance was 1350. five months after he purchased the computer, his balance was 1050. what is an equation that models the balance b after m months

Answers

1800 - 1350= 450 3 months after the purchase he payed $450
450/3= $150 per month

1350 - 1050= 300 5 months AFTER THE PURCHASE he payed $300
300/2= $150 per month
^after 2 more months he payed $300^

$150 per months

Equation: (initial amount) - (150)M
M= amount of months after purchase

B = 1800 - 150M

The equation that models the balance b after m months is b = 1800 - 150m

Initial cost = 1800

Difference in balance = 1350 - 1050 = 300

Number of months used = 5 months - 3 months = 2 months

Therefore, the equation that models the balance b after m months will be:

b = 1800 - (300/2)m

b = 1800 - 150m

Read related link on:

https://brainly.com/question/6068577

x/3 >-1 graph and check solutions

Answers

[tex]\dfrac{x}{3} > -1\ \ \ \ |\cdot3\\\\x > -3\to x\in(-3;\ \infty)[/tex]

Given ∠ABC is a right angle. Prove ∠1 and ∠2 are complementary.
Write a two column Proof.

Answers

m∠ABC = 90 degrees
m∠1 + m∠2 = m∠ABC
Use transitive property of equality
m∠1 + m∠2 = 90 degrees.
According to the definition of complementary angles, ∠1 and ∠2 must be complementary.

Have an awesome day! :)

A cube has a volume of 216 cubic centimeters. What can be concluded about this cube?

Answers

s = edge length
Vol = s^3 = 216

There are 6 faces, each has an area of s^2

volume = 216

side = cubic root(216)

the length of a side = 6 centimeters

Claudia is reading a book that has 360 pages. she read some book last week. She plans to read 46 pages today when she does she will be 4/5 of the qay through the book. How many pages did she read last week?

Answers

4/5 of 360 is 288, but that's how much she read after today so last week she read that much minus 46 which is 242

your answer is 242.
I hope this helps you out.

can a quadrilateral have 4 obtuse angles

Answers

No. It can have at most 2

A quadrilateral cannot have 4 obtuse angles

How to determine the true statement

From the question, we have the following parameters that can be used in our computation:

A quadrilateral

By definition, the sum of angles in a quadrilateral is 360

And an obtuse angle is greater than 90

So, we have

Sum = 4 * greater than 90

Evaluate

Sum = greater than 360

This means that a quadrilateral cannot have 4 obtuse angles

Answers

I think you are missing an x in the equation -3 - 4y= - 23.

If not, then multiply -3x + y = 2 by 4. This will eliminate y.

4(-3x + y) = 4(2)

-12x + 4y = 8
-3 - 4y = - 23

Do you see that 4y and -4y disappear?

-15x = -15

x = -15/-15

x = 1

Can you find y?

How much change will you get back if you bought three $0.99 chocolate bars and paid with a $5 bill

Answers

you will get two dollars

0.99 times 3 is 2.97 and 5.00 subtract 2.97 is 2.03

The change would be $2.03

what does a negative y-intercept mean for real world application?

Answers

Like a person with a $1,000 debt and starts making monthly payments, the money that person owes becomes less and less each month.

Final answer:

A negative y-intercept in a real-world context indicates that the system or condition being measured starts below the baseline or has a deficit to begin with. It can represent an initial loss in economics, such as starting with debt or needing initial investment. The slope of the line is critical to understanding how changes in one variable affect another.

Explanation:

A negative y-intercept in a real-world application can have various implications depending on the context. In many scientific experiments, the y-intercept represents the baseline level of the system without any experimental conditions applied. If the y-intercept is negative, this might indicate that in the absence of a certain factor (represented by the x-variable), the system has a deficit or a reduction in the measured quantity. For instance, if we are plotting a graph of growth over time, a negative y-intercept could imply that there was an initial debt or loss before measurements began.

When it comes to economics and data models, a negative y-intercept on a graph could represent a starting deficit. For example, a company might have initial losses (negative y-intercept) that it seeks to overcome as production (x-variable) increases. Supply and demand models, cost projections, and similar economic graphs can also have negative y-intercepts indicating starting positions below zero on the graph—such as starting with a debt or having to invest before seeing any return.

The y-intercept and the slope (m-term) together specify a particular line on a graph that can offer a reasonable approximation of real-world data. Economists find the slope particularly useful as it shows the relationship between two variables, like how a change in price affects the quantity supplied.

PLZ HELP! IN DESPERATE NEED OF HELP! Thx! Remeber to SHOW ALL OF YOUR WORK! Thx so much! :)

Answers

well everything equals 360 degrees right ? do 128-68 which is 60 then divide that by 2 so x equals 30 and y equals 30.

The cost of a ticket to an amusement park is $42 per person. For groups of up to 8 people , the cost per ticket decreases by $3 for each person in the group .Marcos’s ticket cost $30. Write an solve an equation to find the number of people in Marcos’s group.

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Marco's ticket decreased by twelve dollars. That means his richer was decreased four times. That means, he came with a group of 32 people.

Can someone please help me with this? I will appreciate it

Answers

It’s the third one. I hope this helps out!

What is 212.8 divided by 3.8? Plz Help!!

Answers

easy.

212.8 divided by 3.8 is equivilant to 56. You would solve this by working a long division equation. Please give brainliest, I really need virtuoso.

212.8 divided by 3.8 equals 56. Hope this helped have a good day!

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