A ramp leading to a freeway overpass is 470 feet long and rises 32 feet. What is the angle of inclination of the ramp?

If the ramp is 470 ft long, it was measured along the ramp, so it is the hypotenuse. The rise of 32 ft. is the vertical diference in elevations.

The angle of inclination is thus
sin-132/470 = a little less than 4°.

Well, if we're talking about an inclined ramp, I guess we could say it's got a bit of an uphill battle! To find the angle of inclination, we can use some good old trigonometry. The tangent of the angle is equal to the rise (32 feet) divided by the run (470 feet). So, the angle (θ) is equal to the arctan(32/470). Crunching the numbers, that's about 3.79 degrees. So, this ramp is definitely on the uphill side, but at least it's not straight up to the stars!

To find the angle of inclination of the ramp, we can use trigonometry. The angle of inclination can be determined by finding the arctangent of the ratio between the rise and the run of the ramp.

The rise is the height of the ramp, which is 32 feet. The run is the length of the ramp, which is 470 feet.

So, the angle of inclination can be calculated using the formula:

Angle = arctan(rise/run)

Angle = arctan(32/470)

Using a calculator, we find that the arctan(32/470) is approximately 3.91 degrees.

Therefore, the angle of inclination of the ramp is approximately 3.91 degrees.

To find the angle of inclination of the ramp, we can use the trigonometric function called "tangent." The tangent function relates the angle of inclination to the ratio of the opposite side (height) to the adjacent side (length).

In this case, the opposite side is the rise of the ramp, which is 32 feet, and the adjacent side is the length of the ramp, which is 470 feet.

Using the tangent function:
Tangent(angle) = Opposite side / Adjacent side

Tangent(angle) = 32 / 470

To find the angle, we need to take the inverse of the tangent function (also known as the arctangent or atan function) on both sides:
angle = arctan(32 / 470)

Using a calculator or an online tool that can perform trigonometric calculations, we can find the approximate value of the angle of inclination of the ramp:

angle ≈ 3.819 degrees (rounded to three decimal places)

So, the angle of inclination of the ramp is approximately 3.819 degrees.