i stand 34 metres away from an object 1.9 metres wide. how big will it look. thanks
How big? Do you mean angle of observation?
the angle is subtends is approximately 1.9/(34 ) radians
hi there. i mean how big will the 1.9 metre wide object look from 34 metres away. answer in metres please. or can you give me the mathematical calculation to use to work it out. many thanks for your help.,sue
To determine how big the object will appear from a certain distance, you can use the concept of angular size. The angular size is the angle subtended by the object at the observer's eye.
In this case, you are standing 34 meters away from an object that is 1.9 meters wide. To find the angular size, you need the distance between your eyes (or the distance between your eyes and the observer's point if you are not the observer). Let's assume a typical eye separation of about 6.5 centimeters or 0.065 meters.
First, we calculate the distance between the observer's eye and the object by subtracting the eye separation from the distance to the object:
Distance to object = 34 meters - 0.065 meters = 33.935 meters
Next, we calculate the angular size using the formula:
Angular Size (in radians) = Arctan(0.5 x Object width / Distance to object)
Angular Size (in degrees) = Angular Size (in radians) x (180 / π)
Given that the object width is 1.9 meters, we can calculate the angular size:
Angular Size (in radians) = Arctan(0.5 x 1.9 / 33.935) ≈ 0.027 radians
Angular Size (in degrees) = 0.027 radians x (180 / π) ≈ 1.548 degrees
Therefore, the object will appear to be roughly 1.548 degrees wide when viewed from a distance of 34 meters.
Please note that this calculation assumes ideal conditions, and factors such as the shape of the object, ambient lighting, and visual acuity may affect how the object appears to the observer.