To find the height of the water tank, we can use trigonometry.
Let’s assume that the height of the tank is ‘h’ meters.
From the given information, we have:
Distance from the base of the tank to the observer = 500 meters Angle of elevation = 45 degrees
In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the tank (h), and the adjacent side is the distance from the base of the tank to the observer (500 meters).
Using the tangent function, we can write:
tan(45°) = h / 500
Since the tangent of 45 degrees is 1, the equation simplifies to:
1 = h / 500
To find the value of ‘h’, we can cross-multiply:
h = 1 * 500
h = 500 meters
Therefore, the height of the water tank is 500 meters.