A skateboarding ramp rises from the ground at a 30o angle. If the ramp covers 20 feet on the ground, how long is the inclined surface of the ramp?
The skateboard ramp rises from the ground at an angle of 30 degrees. The ramp covers 20 feet on the ground. Let the length of the inclined surface of the ramp be L.
Using the angle of incline and the distance covered on the ground gives:
cos 30 = 20/L
=> L = 20/cos 30
=> L = `20/(sqrt 3/2)`
=> L = `20*2/sqrt 3`
=> L = `40/sqrt 3`
=> L = 23.094
The length of incline is 23.094 feet.
First draw the figure of a right angled triangle with base 20m and the hypotenuse inclined at 30 degree. The road is the base in this triangle and the Ramp is the Hypotenuse.
Here we need to use trignometry.
Cos 30 will give us the ratio of the length of road to the ramp. Value of cos 30 is (Underroot 3)/ 2.
Let length of ramp be x.
So Cos 30 = Length of road / Length of ramp
(Root 3) / 2 = 20 / x
x = 20 * 2 / (root 3)
= 40 / 1.73(approx value of root 3)
= 23.09 m(approx)
Thus the length of the ramp is 23m (approx).
Please correct me if i am wrong.