You have been asked to build a ramp for Dan’s Daredevil Motorcycle Jump. The dimensions you are given are indicated below. Find the height and incline in feet. Round to the nearest foot
One side is 200 ft.The angle between the hypotenuse and the side of 200 ft is 13 degrees.
Height = ?
Incline (hypotenuse) = ?
Tan13 = h/200
h = 200*Tan13 = 46 Ft.
Cos13 = 200/r
r = 200/Cos13 = 205 Ft = hypotenuse.
To find the height and incline of the ramp, we can use trigonometry.
Given:
One side = 200 ft
Angle = 13 degrees
We can label the sides of the right triangle formed by the ramp as follows:
The side opposite the angle of 13 degrees is the height.
The side adjacent to the angle of 13 degrees is the side with a length of 200 ft.
The hypotenuse of the triangle is the incline of the ramp.
The height can be found using the sine function: sin(angle) = height/hypotenuse
height = sin(angle) * hypotenuse
Using the given values, we can calculate the height as follows:
height = sin(13 degrees) * 200 ft
height ≈ 0.22492 * 200 ft
height ≈ 44.98 ft
The incline (hypotenuse) can be found using the Pythagorean theorem: hypotenuse = √(height^2 + adjacent side^2)
incline = √(height^2 + 200 ft^2)
incline = √(44.98 ft^2 + 200 ft^2)
incline ≈ √(2024.0004 ft^2)
incline ≈ 45.03 ft
Therefore, the height of the ramp is approximately 45 feet, and the incline is approximately 45 feet as well.
To find the height and incline of the ramp, we can use trigonometric functions. In this case, we are given the length of one side (200 ft) and the angle between the hypotenuse and that side (13 degrees).
First, let's find the height of the ramp:
1. Identify the sides of the right triangle:
- The side opposite the angle of 13 degrees is the height (unknown).
- The side adjacent to the angle of 13 degrees is the side with a length of 200 ft.
2. Use the tangent function (tan) to find the height:
- tan(angle) = height / adjacent side
- tan(13 degrees) = height / 200 ft
Rearranging the formula, we have:
- height = tan(13 degrees) * 200 ft
Using a scientific calculator or trigonometric table, evaluate the tangent of 13 degrees, then multiply it by 200 ft to find the height.
Next, let's calculate the incline (hypotenuse):
1. Use the Pythagorean theorem to find the length of the hypotenuse:
- hypotenuse^2 = height^2 + adjacent side^2
- hypotenuse^2 = height^2 + (200 ft)^2
Now we need to take the square root of both sides of the equation:
- hypotenuse = √(height^2 + 200^2)
Using a calculator, find the square root of the sum of the height squared and 200 squared to get the length of the incline or hypotenuse.
Round the height and incline to the nearest foot as specified in the question.
So, by following these steps, you can find the height and incline of the ramp.