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

The length of the third piece of the ramp is;

D. 9.24 feet

Step-by-step 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;

Therefore, we get;

The length of the third piece, r ≈ 9.24 feet

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

answer: 12x^2+6x

step-by-step explanation:

6x does not equal 24x. hope it works!