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) = ?
h t t p : / / i . i m g u r . c o m / S s C g R N Y . png
Please help this is what the triangle looks like. I may have explained it wrong so this will clarify it.
It is safe i promise. it is a picture of what i am explaining
See previous post: Fri, 10-24-14, 5:38 PM.
To find the height and incline (hypotenuse) of the ramp, we can use basic trigonometry principles. In this case, the given information allows us to use the sine function.
First, let's label the sides of the triangle:
- 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 is the incline, which we want to find.
To find the height, we can use the equation:
sin(angle) = opposite/hypotenuse
Substituting the given values, we have:
sin(13 degrees) = height/hypotenuse
Now we can solve for the height by rearranging the equation:
height = sin(13 degrees) * hypotenuse
To find the incline (hypotenuse), we need to solve for it using the Pythagorean theorem:
hypotenuse^2 = height^2 + side^2
We know the side with a length of 200 ft and we have just found the height. Plugging these values into the equation, we have:
hypotenuse^2 = (sin(13 degrees) * hypotenuse)^2 + (200 ft)^2
Expanding this equation, we can solve for the hypotenuse:
hypotenuse^2 = sin^2(13 degrees) * hypotenuse^2 + 40000 ft^2
hypotenuse^2 - sin^2(13 degrees) * hypotenuse^2 = 40000 ft^2
hypotenuse^2 * (1 - sin^2(13 degrees)) = 40000 ft^2
hypotenuse^2 * cos^2(13 degrees) = 40000 ft^2
hypotenuse = sqrt(40000 ft^2 / cos^2(13 degrees))
Now we can calculate the height and incline:
1. Calculate the height:
height = sin(13 degrees) * hypotenuse
2. Calculate the incline (hypotenuse):
hypotenuse = sqrt(40000 ft^2 / cos^2(13 degrees))
Lastly, round the results to the nearest foot, as requested.
I hope this explanation helps you understand how to solve for the height and incline of the ramp.