a road has a steady gradient of 1 in 10. what angle does the road make with the horizontal to the nearest degrees
tan θ = 1 / 10 = 0.1
θ = arctan ( 0.1 ) = tan⁻¹( 0.1 )
θ = 5.7105931375°
θ = 6° to the nearest degrees
Well, if a road has a steady gradient of 1 in 10, it means that for every 10 units you move horizontally, you move 1 unit vertically. So, the ratio of the vertical distance to the horizontal distance is 1/10.
To find the angle, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the vertical distance and the adjacent side is the horizontal distance.
If we let x represent the horizontal distance, then the vertical distance would be x/10. Now, we can find the angle θ:
tan(θ) = (x/10) / x
Simplifying, we get:
tan(θ) = 1/10
To find the angle θ, we can take the inverse tangent (arctan) of both sides:
θ ≈ arctan(1/10)
Using a calculator, we find that θ is approximately 5.71 degrees (rounded to the nearest degree).
So, the angle that the road makes with the horizontal to the nearest degree is 6 degrees.
Now, that's quite a "steep" answer, isn't it?
To find the angle that the road makes with the horizontal, we can use trigonometry. The gradient of the road, which is 1 in 10, can also be expressed in terms of a trigonometric ratio.
The gradient can be written as rise over run, where the rise is 1 unit and the run is 10 units. This forms a right-angled triangle, where the gradient is the opposite side and the horizontal distance is the adjacent side.
We can use the tangent function to find the angle. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Let's calculate the angle using the formula:
Angle = arctan(opposite/adjacent)
Angle = arctan(1/10)
Using a calculator, we can find that the angle is approximately 5.71 degrees.
Therefore, the road makes an angle of approximately 5.71 degrees with the horizontal when it has a steady gradient of 1 in 10.
To find the angle that the road makes with the horizontal, you can utilize the inverse tangent function. The gradient of 1 in 10 means that for every horizontal distance of 10 units, the road rises by 1 unit.
The tangent of an angle is calculated as the opposite side (the rise) divided by the adjacent side (the run). In this case, the rise is 1 unit and the run is 10 units. Therefore, the tangent of the angle (θ) can be expressed as:
tan(θ) = 1/10
To find the angle θ, we can take the inverse tangent (or arctan) of both sides:
θ = arctan(1/10)
Calculating this using a scientific calculator or an online calculator, the angle is approximately 5.71 degrees. Rounding this value to the nearest degree, the road makes an angle of 6 degrees with the horizontal.