Question

A ramp leading to the freeway overpass is 210 feet long and rises 31 feet. what is the measure of the angle formed between the ramp and the freeway?

Answer 1

To find the measure of the angle formed between the ramp and the freeway, we can use trigonometry.

Step-by-step explanation:

To find the measure of the angle formed between the ramp and the freeway, we can use trigonometry. The angle can be found using the inverse tangent function, which relates the length of the side opposite the angle (the rise) to the length of the side adjacent to the angle (the length of the ramp).

We can use the formula:

angle = arctan(rise/run)

In this case, the rise is 31 feet and the run is 210 feet. Plugging these values into the formula, we get:

angle = arctan(31/210)

Using a calculator, we find that the measure of the angle is approximately 8.2 degrees.

Answer 2

When you draw the figure described in the problem, you will see a right triangle where the hypotenuse is the length of the ramp which is 210 feet and the height is 31 feet. To determine the angle formed between the ramp and the freeway, we use a trigonometric function which would be the sine function. We do as follows:

sin (α) = height / hypotenuse
sin (α) = 31 / 210
α = 8.49 degrees