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 Question from MF, a student: Would you have any idea how the 'latitude of 44 degrees N" has anything to do with this question and how I would apply it? The leaning tower of Pisa leans toward the south at an angle of 5.5 degrees. One day near noon its shadow was measured to be 84.02 m long and the angle of elevation from the tip of the shadow to the top of the tower was measured as 32.0 degrees. To answer the question, assume that the tower is like a pole stuck in the ground, it has negligible width. Also, it is important to know that Pisa Italy is at a latitude of approx 44 degrees North because this affects the direction of the shadow.)

Hi there.

This means that if you draw a line from the center of the earth to anywhere on that ring of lattitude on the earth's surface, and also draw a line from the center of the earth to the equator at the same longitude, then the angle between these lines is 44 degrees. The "N" just means this is in the northern hemisphere.

I don't see a question in what you sent, so I am not sure what you are expected to do with this. Are you missing a sentence? I think it must want you to figure out the length of the tower itself (I won't call it a "height" - that would be confusing).

"Near noon" is when the sun is due south or due north (or exactly overhead if you are at the equator). This is because of the way our time zones are structured. For this question, it is important to know if it is north or south. The lattitude 44 degrees north is further north than the Tropic of Cancer, so the sun at noon is always in the South, no matter what season we are in. In the far south (beyond the Tropic of Capricorn), it would always be in the north. Between these latitudes, it would depend on the time of year. These Tropical lines are at about 23 degrees north and south of the equator, by the way.

Okay, so now you know that the sun is south of the tower of Pisa at noon.

Is this enough help for you to work out the rest of the problem? You should be able to get to a point where you can draw a scalene triangle involving the ground, the tower and the sunbeam from the top of the tower to the end of the shadow. You should know two of the angles (so you can find the third if you want it) and you know the length of one side (the shadow). Which trig law (sine law or cosine law) can you use to find the length of the tower itself?

Hope this helps,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.