Question

A crew of piano movers uses a 6.5-foot ramp to move a 990 lb Steinway concert grand up onto a stage that is 1.8 feet higher than the floor. How far away from the base of the stage should they set the end of the ramp so that the other end exactly reaches the stage?

Answer 1

Answer:

• 6.2458 feet.

Explanation:

Lets call the point in which the end of the ramp touches the ground, point A.

Lets call the point of the base of the stage, point B

And lets call the point in which the ramp touches the stage, point C

If the ramp exactly reaches the stage, ABC forms a right triangle, being one cathetus AB, the other cathetus being BC, and being the hypothenuse CA

The length of AB its the distance between the end of the ramp and the base of the stage. This is the distance  we are looking for.

The length of BC its the height of the stage. This is 1.8 feet.

The length of CA its the length of the ramp, This is 6.5 feet.

Now, we can use the Pythagorean Theorem, this is:

$(AB)^2 + (BC)^2 = (CA)^2$

But, as we wanna to find AB, we can write

$(AB)^2 = (CA)^2 - (BC)^2$

$AB = \sqrt{(CA)^2 - (BC)^2}$

Taking the values:

$AB = \sqrt{(6.5 \ ft)^2 - (1.8 \ ft)^2}$

$AB = \sqrt{(6.5 \ ft)^2 - (1.8 \ ft)^2}$

$AB = 6.2458 ft$

And this is how far away the base must be.