There is a stick which is 80cm long.
In summer solstice, the shortest length of the shadow is 15cm.
In winter solstice, the longest length of the shadow is 130cm.
Which latitude does the stick locate?

i want to know the calculation method, thanks....

With a bit of trig, the shadow at noon gives you the angle of the Sun above the horizon as it crosses the meridian (the north-south line).
Comparing the two angles will give you the angle that the sun moves north and south of the equator each year.
Once you know how far north the sun comes in the summer, you can compare that to the altitude in the sky you've already calculated, and deduce your latitude.

Apologies for not doing the calc for you, but I have a sense that I may be helping someone with their homework.

Grant Hutchison

Longest? shouldn't that be "shortest" also? At dawn on the winter solstice, the shadow could get very long.

The summer solstice data alone should be able to give you an answer, as will the winter solstice data (if you know the latitudes of the Tropics). The two answers are approx. the same answer.

80 cm and 15 cm gives you the tangent of the angle involving the stick and the hypoteneuse. That angle is the same as the one that tells you how far off of verticle the sun is at noon. If you know the altitude of the sun at noon on the solstice (or any other day where you know the Sun's declination) you can work backward to your latitude.

You can use the angles for both solstices to split the difference and get the angle for an equinox, though. The equinox angle is your latitude angle. This won't tell you if you are north or south of the equator though. 8)

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-al

I reckon you've been lost for over six months, so I guess no-one's coming to look for you - time to either hike out yourself or settle down where you are.

Are you survivorman? ....Heh check out Outdoor life Network if you don't know who I'm referring to (Les Stroud, in Canada, I can't say for elsewhere!)

Pete

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PJE

There's so much I don't know about astrophysics. I wish I had read that book by that wheelchair guy.