An airship has an altitude of 800 m , in a distance, a village is seen with an angle of depression 12 °. Find the distance of the airship from the village..
review your basic trig function definitions. Draw a diagram, and you will see that
the line-of-sight distance x is given by
800/x = sin 12°
The distance along the ground is given by
800/x = tan 12°
Pick your case, and just solve for x.
To find the distance of the airship from the village given the altitude of the airship and the angle of depression, we can use trigonometry.
Let's denote the distance of the airship from the village as 'd'.
Given:
Altitude of the airship = 800m
Angle of depression = 12°
From the given information, we can visualize a right-angled triangle with the airship above the village. The angle of depression is the angle between the line of sight and the horizontal line. The opposite side of this angle is the altitude of the airship, and the adjacent side is the distance between the airship and the village.
Using trigonometry, the tangent function can relate these sides of the triangle. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Therefore, we can write:
tan(12°) = 800m / d
Now, we need to solve for 'd'. Rearranging the equation, we have:
d = 800m / tan(12°)
Using a calculator, we can find the tangent of 12° and substitute it into the equation:
d ≈ 800m / tan(12°)
d ≈ 800m / 0.212
d ≈ 3773.58m
Therefore, the distance of the airship from the village is approximately 3773.58 meters.