Sure, I can help you solve that math problem step by step.
First, we need to find the length of the hypotenuse of the ramp using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).
So, using that formula, we can calculate the length of the ramp's hypotenuse: c^2 = 4.2^2 + 0.7^2
c^2 = 17.64 + 0.49
c^2 = 18.13
c = sqrt(18.13)
c = 4.26m
Now that we have the length of the hypotenuse, we can use the inverse trigonometric function of sine to find the angle of inclination. The sine of an angle is equal to the opposite side (in this case, the rise of the ramp, which is 0.7m) over the hypotenuse (4.26m).
So, sin(theta) = opposite/hypotenuse
sin(theta) = 0.7/4.26
sin(theta) = 0.1643
Now, we need to find theta by taking the inverse sine of 0.1643 (or sin(theta)).
theta = sin^-1(0.1643)
theta = 9.47 degrees
So the angle of inclination of the ramp to the nearest degree is 9 degrees.