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How can you calculate height of a pyramid by measuring the length of its shadow?
By means of trigonometry if you know the angle of elevation or by comparing it with a nearby object if you know its height and shadow length.
I have no idea how to go about this question on my geometry homework! Can someone help me?
The two triangles shown are similar triangles. Numerically, the ratio computed by dividing the length of any side of tower triangle by the length of the corresponding side of the walking stick (similar) triangle will be the same value. Therefore, when the length of the tower shadow is divided by the length of the walking stick shadow, that ratio will be the exactly same as the tower height divided by the walking stick height. (length of tower shadow)/(length of walking stick shadow) = (tower's height)/(walking stick height) tower's height = {(length of tower shadow)/(length of walking stick shadow)}*(walking stick height)
Is length squared the same as length times height?
No! Length squared will be the length times the length again. Length times height is going to find the area so it will not be the same.
How do you use shadows to measure?
You can use shadows to measure the heights of trees, or buildings, as long as you can make two separate measurements at exactly the same time of day. While one person or group measures the length of the shadow of the tree or other object, another person or group carefully measures the length of the shadow cast by a smaller object, such as a person, sign, or pole.The ratio of the length of the shadow to the height of the object will be the same for almost every object casting a shadow at that particular moment of the day. So divide the known or measured height of a person by the length of his shadow to find this ratio, then multiply the other shadow length by this amount, to give a good estimate of the height of the taller object.Example:A tree's shadow at 5 PM is found to stretch 80 feet from the base of the tree.A boy is known to be 5 feet tall, his shadow at 5 PM is 10 feet long.(So the shadow length of other objects, measured at 5 PM, will all be twice their height.)5 ft/ 10 ft = 0.5 and 0.5 x 80 = 40 tells us the tree itself is about 40 feet tall.
What tool do you use to measure the height of a school?
(1) One way would be to have a stick, stuck vertically into the ground. Measure the length of the shadow and the length of the stick. The actual height of the stick will be a ratio of the shadow's length. Then measure the length of the school's shadow. The height of the school in comparison with its shadow length will be same ratio as the height of the stick compared to its shadow length. You could use a tape measure for this. And possibly a calculator, which will make the calculation easier than doing it by long arithmetic or mental arithmetic. (2) Another way would be to use something that can tell you, from a short distance away from the school, the angle between the top of the school and the ground. A sextant can do this. It is more accurate than using a protractor. Using trigonometry and the distance from the building to where you are standing, you will be able to calculate the height of the school, because it will be at right angles to the line from you to the school. If you don't know trigonometry, method (1) will be easier.
