Question

You are driving up a long, inclined road. After 1.20 mi, you notice that signs along the roadside indicate that your elevation has increased by 550.

(a) What is the angle of the road above the horizontal?
(b) How far do you have to drive to gain an additional 190 ft of elevation?

Answer 1

The angle of the road above the horizontal is approximately 24.8°. To gain an additional 190 ft of elevation, you need to drive approximately 449 ft.

Step-by-step explanation:

To find the angle of the road above the horizontal, we can use trigonometry. The angle can be calculated using the formula arctan(elevation/change in distance). In this case, the angle is arctan(550/1.20). Using a calculator, the angle is approximately 24.8°.

To find the distance needed to gain an additional 190 ft of elevation, we can use the same formula. The distance is equal to the elevation/change in angle. Plugging in the values, the distance is 190/ tan(24.8°), which is approximately 449 ft.