From the top of a building 50m high, the angle of depression of a car is 55degree. Find the distance the car from the foot of the building
d / 50 m = tan(90º - 55º)
solve for d
The answer is d= 34.77m or 1.44= 50/d
To find the distance of the car from the foot of the building, we can use trigonometry.
The angle of depression is the angle that the line of sight from the top of the building makes with the horizontal line.
In this case, the angle of depression is 55 degrees.
Let's call the distance from the car to the foot of the building x.
Using trigonometry, we can set up the equation:
tan(angle of depression) = opposite/adjacent
tan(55 degrees) = 50/x
To find x, we need to solve for it.
Rearranging the equation:
x = 50 / tan(55 degrees)
Using a calculator, we can find:
x ≈ 50 / 1.428148
x ≈ 34.949 meters
Therefore, the distance from the car to the foot of the building is approximately 34.949 meters.
To find the distance of the car from the foot of the building, we can use trigonometry and the concept of angle of depression.
Let's denote the distance from the foot of the building to the car as "x".
We know the height of the building is 50m and the angle of depression is 55 degrees. The angle of depression is the angle between the horizontal line (ground level) and the line of sight from the top of the building to the car.
Now, consider the right triangle formed by the building, the car, and the line of sight. The vertical side of the triangle represents the height of the building (50m), the horizontal side represents the distance from the foot of the building to the car (x), and the angle of depression is the angle between the vertical side and the hypotenuse.
Using trigonometry, we can use the tangent function to relate the angle of depression to the sides of the triangle:
tan(angle of depression) = opposite/adjacent
tan(55 degrees) = 50/x
To solve for x, we rearrange the equation:
x = 50/tan(55 degrees)
Using a scientific calculator or an online tool, the tangent of 55 degrees is approximately 1.428.
Therefore, x = 50/1.428 = 34.93 meters.
So, the distance of the car from the foot of the building is approximately 34.93 meters.