When you see a tall object, such as a tree or a flagpole, you may wonder how tall the object is but not have any way to reach the top to measure the height. Instead, you can use trigonometry to calculate the height of the object. The tangent function, abbreviated "tan" on most calculators, is the ratio between the opposite and adjacent sides of a right triangle. If you know, or can measure the distance from the object to where you are, you can calculate the height of the object.
Measure the distance from the object you want to calculate the height of to where you are standing.
Use the protractor to estimate the angle formed by the line parallel to the ground at your eye level and the line from the top of the object to your eyes.
Use your calculator to find the tangent of the angle from step two. For example, if the angle from step two was 35 degrees, you would get approximately 0.700.
Multiply your distance from the object by the result from step three. For example, if you were 20 feet from the object, you would multiply 20 by 0.700 to get about 14 feet.
Measure the distance from the ground to your eyeball and add the result to the result from step four to calculate the height of the object. For example, if you measure five feet from the ground to your eyeballs, you would add five to 14 to find the total height of the object equals 19 feet.
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