[Math question] Finding the Size of a shadow
Drawmack
First Post
Just look at some shadows in a controlled and vironment and you'll see this.
Use a flashlight in a completely black room.
The floor is the bottom of the triangle, the objects top is the tip of the triangle. So you have a right triangle. Move the light source around and you'll note that if you draw a lin straight to the floor from the light source and straight to the tip of the shadow then back up to the light source you have another right triangle.
These two right triangles change in proportion to one another. Figure out how to calculate either one and you can claculate them both.
This being the case you can also create a function to determine their sizes based on the pivot point, which is the top of the object casting the shadow.
Use a flashlight in a completely black room.
The floor is the bottom of the triangle, the objects top is the tip of the triangle. So you have a right triangle. Move the light source around and you'll note that if you draw a lin straight to the floor from the light source and straight to the tip of the shadow then back up to the light source you have another right triangle.
These two right triangles change in proportion to one another. Figure out how to calculate either one and you can claculate them both.
This being the case you can also create a function to determine their sizes based on the pivot point, which is the top of the object casting the shadow.
Ah, sorry, Drawmack; I consistently misread "right triangle" as "right angle" -- which confused me, but didn't jar me into correctly seeing what you wrote.
Naturally you can form a right triangle from the shadow (as base), the object (as verticle side), and the path of the light (as the hypotenuse); that's why I gave a trigonometric answer in the first place!
Naturally you can form a right triangle from the shadow (as base), the object (as verticle side), and the path of the light (as the hypotenuse); that's why I gave a trigonometric answer in the first place!
Drawmack
First Post
Utrecht said:
Nope, you use the height of the ground at the end point of the shadow, and subtract the difference between the hieght of the ground the object is on and the height of the ground at the end of the shadow from the height of the object, note that if the object is on higher ground then the shadow's tip this would be a negative number and subtracting a negative is equivocal to adding a positive.
Storminator
First Post
Drawmack said:
Utrecht is correct. The right angle in your right triangle is between the verrtical object casting the shadow and the ground. If the ground isn't level, or the object isn't vertical, the angle isn't right, an neither is the triangle.
If the casting object is height H, the angle between the light source and vertical is A, and the angle between the ground and the object is B, the shadow length L is:
L = H *sin(A)/sin(180-A-B)
Note that when both A = B = 90, sin(180-A-B)=0 and shadow length is infinite.
Determining the angle the sun makes with the vertical as a function of time of day, latitude, and time of year is left as an exercise for the reader, as are corrections for curvature of the earth.
PS
Dareoon Dalandrove
First Post
Thanks for the great answers. Using the right triangle method as perposed byu Drawmack there is still too many unknowns though. If the height is 6ft that still leaves two of the side unknown, which you would need one more of to complete the equation.
Saeviomagy
Adventurer
Simply put, if you can't do the trig yourself, just pick a number.
Shadows will have the following heights
Midday: 0
1/3 of the way through morning, or 2/3rds of the way through afternoon: twice the height of the caster
Halfway through morning or afternoon: Height of the caster
2/3rds of the way through morning or 1/3rd of the way through afternoon: half the height of the caster
Just after dawn or just before sunset: 5 to 10 times the height of the caster.
Shadows will have the following heights
Midday: 0
1/3 of the way through morning, or 2/3rds of the way through afternoon: twice the height of the caster
Halfway through morning or afternoon: Height of the caster
2/3rds of the way through morning or 1/3rd of the way through afternoon: half the height of the caster
Just after dawn or just before sunset: 5 to 10 times the height of the caster.
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