Question

Your towns public library is building a new wheelchair ramp to its entrance. By law the maximum angle of incline for the ramp is 4.76 degrees. The ramp will have a vertical rise of 2 ft. What is the shortest horizontal distance that the ramp can span?

Answer 1

For this case we can model the problem as a rectangle triangle.
 We have the angle between the base and the hypotenuse of the triangle.
 We have the height of the triangle.
 We want to calculate the base of the triangle.
 For this, we use the following trigonometric relationship:
 $tan (4.76) = 2 / x$
 Clearing x we have:
 $x = 2 / tan (4.76) x = 24.02 feet$
 Answer:
 the shortest horizontal distance that the ramp can span is:
 x = 24.02 feet

Answer 2

By using trigonometric ratio we got that if the maximum angle of incline for the ramp is 4.76 degrees. The ramp will have a vertical rise of 2 ft. then the shortest horizontal distance that the ramp can span is 24 ft.

What are trigonometric ratios?

Relation between angle and ratio of sides are known trigonometric ratios.

Here given that maximum angle of incline for the ramp is 4.76 degrees. The ramp will have a vertical rise of 2 ft.

Now we can say that

$\text{tan(4.76\textdegree )} = \frac{2}{x} \\\\0.083269= \frac{2}{x} \\\\x= \frac{2}{0.083269} \\\\x= 24.0185\\\\x\approx24 ft.$

By using trigonometric ratio we got that if the maximum angle of incline for the ramp is 4.76 degrees. The ramp will have a vertical rise of 2 ft. then the shortest horizontal distance that the ramp can span is 24 ft.

To learn more about  trigonometric ratio visit : https://brainly.com/question/24349828