Usiing angles and height to calculate height/altitude of object

[moonman239]

Pre-requisite: Protractor
Requirement: Both the measurers and the object should be perpendicular to the ground

One-Person Method: Find point A, the point whose vertical distance to the ground you want to measure. If you're measuring the height of an object, this will be the top of the object. If you're measuring the altitude of the object, this will be the bottom of the object.Measure the angle of elevation from your head to point a. Call that angle A. Then measure the angle of elevation from the bottom of your feet to the top of the object. Call that angle B.

The first thing to do is calculate d, the horizontal distance between you and the object. d = your height / ((tan(A) - tan(B)).
Then use trigonometry to solve for h, the distance from point a to the ground. (If you want to know the height of an object - as in the distance between the top of the object to the bottom - and the bottom is higher than your feet - you'll need to subtract the vertical distance from the top of the object to the ground from the vertical distance from the bottom of the object to the ground.) Since tan(A) = h/d, d*tan(A) = h.

 

[jvicens]

Hello! Thank you for sharing this method for measuring vertical distances and angles using a protractor. It seems like a practical and efficient way to obtain accurate measurements. However, I would like to suggest a few modifications to ensure that the requirement of perpendicularity is met.

Firstly, instead of just measuring the angle of elevation from your head to point A, it would be better to use a plumb line or a level to ensure that your measuring device is perfectly perpendicular to the ground. This will eliminate any potential errors caused by an uneven surface or an incorrect angle of elevation.

Secondly, when measuring the angle of elevation from your feet to the top of the object, it would be best to use a tripod or a stable base to ensure that the protractor is also perpendicular to the ground. This will help to maintain consistency and accuracy in your measurements.

Lastly, I would also recommend using a laser level or a spirit level to ensure that the object itself is perpendicular to the ground. This will help to eliminate any potential errors caused by an uneven or sloping surface.

Overall, incorporating these modifications into your method will help to ensure that both the measurer and the object are perfectly perpendicular to the ground, meeting the required prerequisite. Thank you again for sharing your method and for considering these suggestions.