Stars and Galexies

2. (3) Suppose you live on planet X. One day the Sun is directly over a place 250 km to you south, while at your position the Sun’s direction is 10 degrees off the vertical. What is the radius of planet X?


Help?

I'm pretty sure this is correct, but it's been a while since I took trig. ^^;



I hope the horribly inaccurate diagram makes sense. Basically, the 10* position of the sun off the horizontal corresponds to the angle of the arc. Since you are given the arc length, you just have to divide the arc length by the angle to find the radius. Just remember that the 10* is in radians.

Here's what I got:

The sun is shining directly on a place 250km south. That spot is the vertical. Take the fraction of the circle and times that by the distance from the vertical spot to your location. That's the circumference. Divide that by pi to get the diameter, divide that by 2 to get the radius. So:

10 degrees = a tenth of a circle = 10/360

Tenth of a circle = 360 divided by 10 = 36 degrees.

36*250km = circumference = 9000km

9000km / pi = diameter = 2866.242038km

2866.242038km / 2 = radius = 1433.121019km

Please tell me if my math is off, but that's the formula I'm supposed to use. So do the numbers add up, or am I way off?

The numbers add up. :D

10* x (3.14/180) = 0.0174444444 <=== converting degrees into radians

250/0.0174444444 = 1433.121019

I've never seen it done that way, before. o_o It makes sense, though.

What level math is this for?