NO.
Because the length of your shadow, is dependent on the position of the sun. The higher the sun is in the sky, the shorter your shadow is. When the sun is low on the horizon in early morning or late evening, you present a larger 'image' and therefore your shadow is bigger.
To find the height of the tree, we can set up a proportion using the similar triangles formed by the tree and its shadow, and the person and their shadow. The ratio of the height of the tree to its shadow is the same as the ratio of the height of the person to their shadow. This gives us (height of tree)/(9 ft) = (6 ft)/(4 ft). Solving for the height of the tree, we get height of tree = (9 ft * 6 ft) / 4 ft = 13.5 ft.
3 yards in height
The closer the light source the larger is the shadow. You can understand this effect using the paraxial aproximation of light theory. If you draw lines from the light source to the edges of an object, there is an angle (call it alpha) between the these lines and the orthonormal vector to the object. The shorter the distance between the light and the object, the higher is alpha (because the height of the object is always the same): tan(alpha) = (height of the object)/(distance between light and object) Of course the relationship between the height of the shadow and the angle is the same: tan(alpha) = (height of the shadow)/(distance to the wall in which the shadow is proyected) So, the higher the angle alpha (and closer the distance between light and object), the heigher is the shadow.
It's not possible to give you an answer without knowing the height of your shadow, because the height of a shadow depends on the position of the light (the lower the longer the shadow is). But if the shadow is exactly the same height as you, it would be the same inches in height as you are. To calculate that, just multiply 5 ft x 12, which = 60 inches, then add the other 3 inches to it. That would give you a total of 63 inches.
Both. At sunrise and sunset on a sunny day, your shadow will be very long. As the sun rises and approaches it's zenith at noon, your shadow becomes progessively shorter, then lengthens again throughout the afternoon.
A sphere's height will always be the same as its diameter.
no
The height of the tree is in direct proportion to the pole and its shadow
The ratio of the height of the object to its shadow are the same for both objects. So, if H is the height of the tower, then H/500 = 40/36 therefore H = 500*40/36 = 555.55... feet.
No only sometimes
No