Random HomeWork Help --- Sun Angle

[CrazyImpling]

Okay, so I have this project in science and I need to find the Sun Angle of Sedona (or On Sedona, whichever works.) Any clue where I can find it? Wikipedia doesn't have it.

 

[Pineapple]

As in the angel the suns rays hit a place called Sedona?

I am in no way Science-y. BUT!

Think of the place in relation to the Equater. The Equater is level with the sun, so the sun it always right above the equater.

...Hum... this makes me think of trig

 

[PurgeandFire]

Then again, earth tilts on its axis, so...

 

[Pyrogasm]

Sedona as in Sedona, Arizona?

At any rate, you can do it the same way the ancient Greeks did, except this time you know different values:

You need to know the distance from Sedona to the Equator and either the circumference of the Earth or the radius of the Earth. Then, look up Eratosthenes and find out how he found the circumference of the Earth using the angle the sun's rays hit the earth at in 2 different places (At the equator it would be 90˚).

It's rather simple.

 

[Andrewgosu]

Looks like someone skipped some basic math lessons...


OK, here it goes.

First, take a random upright stick, go outside and jam it into the ground, making a 90 degree angle with the Earth's surface. After that, measure the stick's length.

(e.g 10 cm)

Next, measure the length of the shadow.

(e.g 16 cm)

As you can see from the picture, a right triangle formed. A little bit of knowledge tells us that, (basic trigonometric functions)

, from which we can derive the angle of the Sun.


But something is a miss! How can we get our hands on the length of the hypotenuse?

Now comes to play the Pythagorean theorem,

, where the length of the hypotenuse equals to the square root of a^2 + b^2.

(e.g

side a was 10 cm (the length of the stick), side b (the shadow) was 16 cm.

square root of 10^2 + 16^2 is roughly about 18.6 cm)

Now we know the length of the hypotenuse.


After that, we can calculate sin (alfa), which is 10 / 18.6 = 0.5376.

Next, just calculate the angle (alfa) using your computer (should have a sin^-1 marking, the button to calculate), which is roughly about 32 degrees 30 minutes (it gives you an irrational number, I already did the conversion to degrees).


Try it yourself!

NB! The angle of the Sun depends on the time of the day, too! Not to mention the current season.



P.S I need a cookie. Hope I got everything right.

 

[PurgeandFire]

Wow Andrewgosu, you sound like a math book or something. xD

 

[Andrewgosu]

Hehe, math can be interesting and useful at the same time!