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.
Can you please help sir
Thnks
tan ß = 40/600 ,(same as slope)
ß = arctan (40/600) = 3.8 degrees
Of course! To find the angle of inclination of the road, we can use basic trigonometry. The angle of inclination (θ) is defined as the arctangent of the rise (opposite side) divided by the run (adjacent side).
In this case, the rise is 40 cm and the run is 6 m. To make the units consistent, we need to convert the rise to meters. Since 1 meter is equal to 100 centimeters, we divide the rise by 100 to get the rise in meters. Thus, the rise is 0.4 meters.
Now we can plug these values into the arctangent formula:
θ = arctan(0.4 / 6)
To calculate this using a scientific calculator or an online calculator, follow these steps:
1. Press the "arctan" or "tan^-1" key on your calculator.
2. Enter the fraction 0.4 / 6.
3. Press the "equals" button to get the result.
The angle calculated will be in radians. To convert it to degrees, multiply by 180 and divide by π (approximately 3.14159).
θ ≈ 3.96 degrees (rounded to the nearest tenth of a degree)
Therefore, the angle of inclination of the road is approximately 3.96 degrees.