A wooden board is placed so that it leans against a loading dock to provide a ramp. The board is supported by a metal beam perpendicular to the ramp and placed on a 1 ft. tall support. The bottom of the support is 9 feet from the point where the ramp meets the ground. The slope of the ramp is 2/5 (this means that for every 2 feet it goes up, it goes 5 to the side). Find the length of the beam to the nearest hundredth of a foot. Note that the 1 ft. support is vertical, but the metal beam is not.

Question

Remember a slope of 2/5 means that everytime you go horizontal 5 units, you go vertical 2 units. (So at 10 units, it should be vertical 4 units, and at 15 it should be vertical 6 units, etc.) Also remember that perpendicular lines have an opposite slope...so if a line has a slope of 1/3, then its perpendicular line will have a slope of -3/1.

Find the distances and plot the points, so you can use the distance formula on the points on either side of the metal beam to find its length! Look for any possible way to find the information you need!

Do the problem step by step, showing your work and explaining what you did to find the answer (the drawings here will help, but make your own--you do not need to submit your drawing, you only need to use it for your own reference). On three of the steps, "prove" what you're doing by stating the theorem or definition you're working with. (You must have three separate proofs--using the distance formula three times doesn't count!)

I am so confused. Please, help.