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# Closer to the sun?

## Question

Micah, Erica, Tomas are standing outside, shoulder to shoulder. Micah has a shadow that is 20ft in length, Tomas has a shadow that is 17ft in length, and Erica has a shadow that is 24ft in length. Assuming that each person's shoulders makes a line segment then the sun is hitting the back of their head 45 degrees off their shoulders.

If it is 5pm:

how tall is each person?

how wide are their shoulders?

Who is closest to the sun?

## 2 answers to this question

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bonanova    76

Are we approximating the people as (2-dimentional) rectangles, whose shadows are characterized by a single length?
What does 45 degrees off their shoulders on the back of their heads signify?

Is that shadow length then a trigonometrically weighted sum of their height and width?

Do we know whether the shoulders have the same proportionality to height for each person?

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Are we approximating the people as (2-dimentional) rectangles, whose shadows are characterized by a single length?

shadows are a single length (focusing on the peak of the shadow). It can be done using rectangles.

What does 45 degrees off their shoulders on the back of their heads signify?

Assuming the sun settles in the west (true west) and they are facing a direction such that if their shoulders were a line segment and their eyes are perpendicular to their shoulder line segment then the sun is shining through as an angle bisector.

Is that shadow length then a trigonometrically weighted sum of their height and width?

height and width would both matter, consider the angle of the sun (assume that it arises at 6am in true east and sets at 6pm and is perfectly straight above at noon)

Do we know whether the shoulders have the same proportionality to height for each person?

let's assume so.

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