A sun's rays are vertical at the point A on a planet. At the point B, which is 265 miles due north of A, the angle of the sun measured to be 7.2 degrees . See the figure. Use this information to approximate the radius and circumference of the planet.
Round to the nearest integer as needed.

Question

Sayedfamily5 Sayedfamily5

25-09-2022
Mathematics

Answered

A sun's rays are vertical at the point A on a planet. At the point B, which is 265 miles due north of A, the angle of the sun measured to be 7.2 degrees . See the figure. Use this information to approximate the radius and circumference of the planet.
Round to the nearest integer as needed.

Answer :

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MrRoyal MrRoyal · Answer 1 · 2022-09-26T15:08:57-04:00

The approximate radius and circumference of the planet are 2109 miles and 13250 miles, respectively

How to use the information to approximate the radius and circumference of the planet?

The given parameters are

Angle, x = 7.2 degrees

Arc length = 265 miles

The arc length is calculated as

Arc length = x/360 * 2πr

So, we have

7.2/360 * 2πr = 265

Multiply through by 360/7.2

So, we have

2πr = 265 * 360/7.2

Evaluate the product

So, we have

2πr = 13250

The above represents the circumference

i.e. C = 2πr

Divide both sides of 2πr = 13250 by 2π

So, we have

r = 13250/2π

Evaluate

r = 2109

Hence, the approximate radius and circumference of the planet are 2109 miles and 13250 miles, respectively

Read more about circumference at

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jcherry99 jcherry99 · Answer 2 · 2022-09-26T20:59:34-04:00

Answer:

Step-by-step explanation:

Comment

This is a set up for a proportion. Part of the circle is cut off by the central angle which is 7.2 degrees. The proportion is set up below

7.2/360 represents how much of the circumference? Are told that it is 265 miles. So we have 3 out of the four parts of the proportion. The steps are

Cross multiply
Solve for 2*pi*r which gives you the circumference
Divide by 2 pi which gives you the radius

Solution

7.2 / 360 = 265 / 2*pi * r Cross Multiply

7.2 * (2*pi*r) = 265 * 360 Combine the right

7.2 * (2*pi*r) =95400 Divide by 7.2

2*pi*r = 95400/7.2

2*pi*r = 13250 This is the circumference. Divide by 2*pi

r = 13250/(2*3.14)

r = 2110 miles This is the radius

A​ sun's rays are vertical at the point A on a planet. At the point​ B, which is 265 miles due north of​ A, the angle of the sun measured to be 7.2 degrees . See the figure. Use this information to approximate the radius and circumference of the planet. Round to the nearest integer as needed.

Answer :

How to use the information to approximate the radius and circumference of the planet?

Other Questions

A sun's rays are vertical at the point A on a planet. At the point B, which is 265 miles due north of A, the angle of the sun measured to be 7.2 degrees . See the figure. Use this information to approximate the radius and circumference of the planet.
Round to the nearest integer as needed.