In a water park, people walk up a ramp before diving into the water below. If they cover a horizontal distance of 100 meters before diving down 50 meters, what is the angle made by the ramp with the ground?
tan Theta = 50/100
Theta = 26.6 degrees
To find the angle made by the ramp with the ground, we can use trigonometry. The angle can be determined by taking the inverse tangent (arctan) of the ratio of the height to the base.
In this case, the height is the vertical distance of 50 meters and the base is the horizontal distance of 100 meters.
The formula to find the angle is:
angle = arctan(height/base)
Substituting the given values:
angle = arctan(50/100)
Calculating this using a scientific calculator or an online calculator, we find that the angle is approximately 26.57 degrees.
To find the angle made by the ramp with the ground, we can use trigonometry. The angle we are looking for is the angle between the ramp and the horizontal ground.
First, let's define the sides of a right triangle formed by the ramp, the ground, and a vertical line from the top of the ramp to the water:
The horizontal distance covered by the ramp is the base of the triangle, so we can label it as "adjacent" (A) = 100 meters.
The vertical distance from the top of the ramp to the water is the height of the triangle, so we can label it as "opposite" (O) = 50 meters.
We can use the tangent function to find the angle:
tan(angle) = O/A
Plugging in the values:
tan(angle) = 50/100
Simplifying:
tan(angle) = 0.5
To find the angle, we need to take the arctan (inverse tangent) of both sides:
angle = arctan(tan(angle)) = arctan(0.5)
Using a calculator or reference table, we find:
angle ≈ 26.565 degrees
Therefore, the angle made by the ramp with the ground is approximately 26.565 degrees.