Person is 1.8 meters tall standing far away at angular height of 5 meters. How do I find how far way they are
angular height of 5m? what is angular height? Do you mean an angle of elevation of 5 degrees to their head? Better add some information here as presented in the problem.
Sorry, I meant to put say the person is 1.8 meters tall and they are standing far enough away to have an angular height of 5 degrees. The question then is how far away is the person.
tan 5 = 1.8/x
To find how far away a person is when their angular height and actual height are known, you can use a basic trigonometric concept called tangent.
First, we need to understand the relationship between the actual height, the distance, and the angular height. The tangent of an angle is the ratio of the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the actual height of the person and the adjacent side is the distance from the person.
Let's denote the actual height of the person as "h" and the distance from the person as "d." The angular height can be thought of as the angle from the observer's line of sight to the top of the person's head.
Now, we can set up the following equation:
tangent(angle) = h / d
In this case, the angle is given as 5 meters and the actual height is given as 1.8 meters. Rearranging the equation to isolate "d," we can solve for the distance:
d = h / tangent(angle)
Plugging in the values for the actual height (h = 1.8 meters) and the angle (angle = 5 meters), you can calculate the distance using a scientific calculator or trigonometric functions available in programming languages.
Using the tangent function, the equation becomes:
d = 1.8 / tan(5)
Calculating this, we get the approximate distance as follows:
d ≈ 1.8 / 0.087
d ≈ 20.68 meters
Therefore, the person is approximately 20.68 meters away.