Dedrea is making a bike ramp on the sidewalk in front of their house. They place a wood plank on top of blocks to form the ramp. The blocks are one foot in height, and the distance from the base of the blocks to where the wood plank touches the sidewalk is five feet. What is the approximate angle formed between the sidewalk and the base of the ramp?
To find the angle formed between the sidewalk and the base of the ramp, we can use trigonometry.
First, we need to find the length of the ramp (hypotenuse). This can be found using the Pythagorean theorem:
(length of ramp)^2 = (height of blocks)^2 + (distance from base of blocks to where the plank touches the sidewalk)^2
(length of ramp)^2 = 1^2 + 5^2
(length of ramp)^2 = 1 + 25
(length of ramp)^2 = 26
length of ramp ≈ √26 ≈ 5.1 feet
Now we have all three sides of the right triangle formed by the ramp, sidewalk, and base of the blocks. Using the tangent function:
tan(θ) = opposite/adjacent
tan(θ) = height of blocks / distance from base of blocks to where the plank touches the sidewalk
tan(θ) = 1 / 5
θ = arctan(1/5)
θ ≈ 11.3 degrees
Therefore, the approximate angle formed between the sidewalk and the base of the ramp is approximately 11.3 degrees.