Question

3. Two students who live on planet X. They want to estimate the circumference. The two students synchronize their watches before one student leaves on vacation 600 miles due west to their home. They notice a 3 degree difference in altitude of the sun at local noon. What is the circumference of the planet?

Answer 1

C = 1256.63 miles

Step-by-step explanation:

This problem is solved by using the following formula for the relation between the arc length of a circle and its radius:

`s=r\theta`

s: arc length

r: radius

In this case "s" is 600 miles, and the angle of the arc length is 3°. With this information you can calculate the radius of the planet X:

`r=(s)/(\theta)=(600miles)/(3\°)}=200\ miles`

With the value of the radius of the planet you can calculate the circumference, by using the following formula:

`C=2\pi r=2\pi (200\ miles)=1256.63\ miles`