A truck driver estimates that a country road rises 40 cm for every 6 m along the road.What is the angle of inclination of the road? Express your answer to the nearest tenth of a degree.
To find the angle of inclination of the road, we can use trigonometry. The angle of inclination can be determined by finding the ratio of the vertical rise to the horizontal distance along the road.
Given that the road rises 40 cm for every 6 m, we need to convert the measurements to the same unit. Let's convert 6 m to centimeters:
1 m = 100 cm
So, 6 m = 6 * 100 cm = 600 cm.
Now, we have the vertical rise of 40 cm and the horizontal distance of 600 cm.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the tangent of the angle of inclination is:
tan(angle) = vertical rise / horizontal distance
tan(angle) = 40 cm / 600 cm
Now, we can solve for the angle by taking the inverse tangent (arctan) of this ratio:
angle = arctan(40 cm / 600 cm)
Using a calculator or mathematical software, we find:
angle ≈ 3.8 degrees (rounded to one decimal place).
Therefore, the angle of inclination of the road is approximately 3.8 degrees.