The angle of elevation is the angle between an imaginary horizontal line and a person's line of sight focused on an object above that horizontal. A line can be drawn from the object to the horizontal, creating a 90-degree angle. The person, the object and the intersection of the object's line and the horizontal create the three points of a right triangle. Using the angle of elevation and the height of the object from the horizontal, you can find the distance between the person and the object.
Calculate the tangent of the angle to find the horizontal distance between objects. Let's say the measurement of the angle is 60 degrees. The tangent of 60 degrees is √3 or 1.732.
Divide the height of the object by the tangent of the angle. For this example, let's say the height of the object in question is 150 feet. 150 divided by 1.732 is 86.603. The horizontal distance from the object is 86.603 feet.
Calculate the sine of the angle to find the total distance between objects, or the hypotenuse. For the example, the sine of 60 degrees is √3/2 or 0.866.
Divide the height of the object by the sine of the angle. For the example, dividing 150 by 0.866 results in 173.205. The total distance between the objects is 173.205 feet.
About the Author
Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.