Question

you are driving along the highway and see a sign indicating that you are about to enter a downhill slope of 10%. you realize that you are going to travel downward at an angle of degrees to the horizontal. (enter your answer as a mathematical expression or with at least two digits beyond the decimal point.) hint: a descent of 10% means that you are going to descend by 1 foot for every ten feet that you travel in a horizontal direction. the angle of your descent is the acute angle that the highway makes with a horizontal line. draw a picture and use an inverse trig function.

Answer 1

The angle of descent on the highway is approximately 5.71 degrees.

Step-by-step explanation:

To find the angle of descent, we need to determine the angle at which the highway makes with a horizontal line. Trigonometry can help us solve this problem. We know that a descent of 10% means that for every ten feet traveled horizontally, we descend one foot vertically.

We can represent this as a right triangle, where the horizontal leg is 10 units and the vertical leg is 1 unit. The angle of descent, which we want to find, is the acute angle between the horizontal leg and the hypotenuse. Using the inverse tangent function, we can calculate this angle:

Angle of descent = arctan(vertical leg / horizontal leg) = arctan(1/10) ≈ 5.71 degrees