Part a:
Let's express this as a fraction, where the rise is the numerator and the run is the denominator. The rise is 1 unit of height, and the run is 10 units of distance. Therefore, the gradient can be expressed as: 1/10
To find the angle that the road makes with the horizontal using trigonometry is: tan θ = 1/10
Solving for θ, we get:
θ = tan^(-1)(1/10) ≈ 5.7 degrees
Therefore, the road makes an angle of approximately 5.7 degrees with the horizontal.
Part b:
If the car drives 2 km along the road, we can use the angle calculated in part a to find the vertical height that the car has climbed. We know that the distance covered along the road is the run, which is 2 km or 2000 meters.
Using trigonometry again, we can find the vertical height climbed by the car, which is the opposite side. The tangent of the angle is: tan θ = 1/10
Let's rearrange this to solve for the opposite side, which is the vertical height climbed:
opposite side = adjacent side x tan θ
opposite side = 2000 x tan (5.7 degrees)
opposite side ≈ 200 meters
Therefore, the car has climbed approximately 200 meters vertically along the inclined road.