Question

Andrew is building a ramp for a snowboarding competition. The rules of the competition say that the height of the ramp must be 8 feet. Andrew has decided to make the base of the ramp and the piece of the ramp that forms the height meet at a 90° angle. The third piece of the ramp will be a straight line connecting the highest point of the ramp to the furthest point of the base, forming a 30° angle across from the 8 foot piece of the ramp. What will be the length of the third piece of the ramp? A. 16 feet B. 10 feet C. 13.86 feet D. 9.24 feet

Answer 1

The length of the third piece of the ramp is;

D. 9.24 feet

Explanation:

The given parameters are;

The height of the ramp = 8 feet

The angle between the piece that forms height and the base = 90°

The angle formed by the third piece connecting the height of the ramp to the furthest point and the 8 foot piece = 30°

Let 'y' represent the 8-foot piece forming the height, and let 'r' represent the third piece, by trigonometric ratio, we have;

`cos(30^(\circ)) = (y)/(r)`

Therefore, we get;

`cos(30^(\circ)) = (8)/(r)`

`r = (8 \ feet)/(cos(30^(\circ))) = (8 \ feet)/((√(3) )/(2) ) = (16 \cdot √(3) \ feet)/(3) \approx 9.24 \ feet`

The length of the third piece, r ≈ 9.24 feet