Johnny is building a ramp to his front door, which is 4.3 feet off the ground. He wants the angle of elevation of the ramp to be 2 degrees. How long will his ramp be?
length = 4.3 ft / sin(2ยบ)
4.3/ramp=sin2 deg
now using the small angle approximation
sin2 deg=(2/360) *2PI= 0.034906585
ramp=4.3/.035=123 feet
check my calculations
To find the length of the ramp, we can use trigonometry. Specifically, we can use the tangent function to relate the angle of elevation to the ratio of the opposite side (the height of the front door) to the adjacent side (the length of the ramp).
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the angle of elevation is 2 degrees and the height of the front door is 4.3 feet. Let's denote the length of the ramp as 'x'.
Using the tangent function, we can set up the equation:
tan(2 degrees) = 4.3 feet / x
To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by x:
x * tan(2 degrees) = 4.3 feet
Now, divide both sides of the equation by tan(2 degrees):
x = 4.3 feet / tan(2 degrees)
Using a scientific calculator or an online calculator, calculate the value of tan(2 degrees) and then divide 4.3 feet by that value to find the length of the ramp.