Measuring Distance with Vectors: Tips and Tricks for Physics Students"

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To measure the distance from a physics laboratory to an outside feature without leaving the building, students can utilize a protractor, meter stick, and vector diagrams. By measuring the angle to the top of the object from two different points—next to the window and 1 meter away—they can create a right triangle scenario. This method allows for the application of trigonometric functions to calculate the distance, despite initial concerns about unknown variables. The key is to establish a relationship between the measured angles and the distances involved. This approach can yield an accurate estimate within 10% for distances less than half a mile.
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The problem reads:
"See if you can devise a METHOD (not a numerical answer) of measuring the distance from your physics laboratory to some outside feature (flag-pole, church steeple, etc.) WITHOUT leaving the building. If the object is less than a half-mile distant the job can be done within about 10%, using ONLY a protractor, meter stick, and drawing a vector diagram to scale."

I understand vectors and all, and I understand what the question is asking. I've tried working out trig functions on paper (since this is a right triangle in which you can measure the angle from the ground to the top of the "outside feature"), but there are just too many unknown variables to actually come up with an equation or relationship among them.

I would much appreciate any suggestions or assistance!
 
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What if you measured the angle to the top of the object from next to the window and then 1 meter away from the window?
 
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