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) = ?
Well, it seems like Dan is really going for it with this daredevil motorcycle jump! Let's see what we can do to build him a ramp.
First, we need to find the height and incline of the ramp, rounding to the nearest foot.
Given that one side is 200 ft and the angle between the hypotenuse and the side of 200 ft is 13 degrees, we can use some fancy trigonometry here.
The height of the ramp can be found using the equation:
Height = side * sin(angle)
So, plugging in the values, we have:
Height = 200 ft * sin(13 degrees)
Calculating it, we get:
Height = 200 ft * 0.224951
Height ≈ 44.99 ft
Now, let's find the incline (the hypotenuse) of the ramp. We can use the Pythagorean theorem to find it.
Using the equation:
Incline^2 = side^2 + height^2
Plugging in the values, we have:
Incline^2 = 200 ft^2 + 44.99 ft^2
Calculating it, we get:
Incline^2 ≈ 40,000 ft^2 + 2,024.4501 ft^2
Incline^2 ≈ 42,024.4501 ft^2
Taking the square root of both sides, we have:
Incline ≈ √42,024.4501 ft^2
Incline ≈ 205 ft
So, rounding to the nearest foot, the height of the ramp is approximately 45 ft and the incline (hypotenuse) is approximately 205 ft.
Good luck to Dan with his daredevil motorcycle jump! Just make sure to keep the clowns out of the way! 🤡
To find the height and incline of the ramp, we can use trigonometric functions.
Given that one side of the ramp is 200 ft and the angle between the hypotenuse and the side of 200 ft is 13 degrees, we can use the sine function to find the height.
sin(angle) = opposite/hypotenuse
sin(13 degrees) = height/200 ft
To find the height, we can rearrange the formula:
height = sin(13 degrees) * 200 ft
Using a scientific calculator or an online trigonometric calculator, we can find the sine of 13 degrees, which is approximately 0.2249510565.
height = 0.2249510565 * 200 ft
height = 44.99021129 ft
Therefore, the height of the ramp is approximately 45 ft.
To find the incline (hypotenuse), we can use the cosine function:
cos(angle) = adjacent/hypotenuse
cos(13 degrees) = 200 ft/hypotenuse
To find the hypotenuse, we can rearrange the formula:
hypotenuse = 200 ft / cos(13 degrees)
Using a scientific calculator or an online trigonometric calculator, we can find the cosine of 13 degrees, which is approximately 0.9702957263.
hypotenuse = 200 ft / 0.9702957263
hypotenuse = 206 ft
Therefore, the incline (hypotenuse) of the ramp is approximately 206 ft.
To find the height and incline of the ramp, we can use trigonometry, specifically the sine and cosine functions.
First, let's label the sides of the right triangle formed by the ramp:
- Let "H" represent the height.
- Let "I" represent the incline (the hypotenuse).
- Let "S" represent the side of 200 ft.
We are given the angle between the hypotenuse (I) and the side of 200 ft, which is 13 degrees.
Using the sine function, we can find the height:
sin(angle) = opposite / hypotenuse
sin(13 degrees) = H / I
Rearranging the formula, we get:
H = I * sin(13 degrees)
Using the cosine function, we can find the side adjacent to the angle, which is the incline:
cos(angle) = adjacent / hypotenuse
cos(13 degrees) = S / I
Rearranging the formula, we get:
I = S / cos(13 degrees)
Now, we can substitute the given values into the formulas to find the height and incline of the ramp.
Height:
H = I * sin(13 degrees)
H = (200 ft) * sin(13 degrees)
H ≈ 46 ft (rounded to the nearest foot)
Incline:
I = S / cos(13 degrees)
I = (200 ft) / cos(13 degrees)
I ≈ 207 ft (rounded to the nearest foot)
Therefore, the height of the ramp is approximately 46 feet, and the incline is approximately 207 feet.