Question

You are driving up an inclined road. After 2.4km you notice a roadside sign that indicates that your elevation has increased by 160m. What is the angle of the road above the horizontal?

Answer 1

The angle of the road above the horizontal is found using trigonometry, specifically the tangent function, which is the ratio of the elevation gain to the distance traveled along the road. By applying the arctan function to 160m/2400m, we can calculate the angle of inclination in degrees.

Step-by-step explanation:

The question involves finding the angle of the road above the horizontal when the elevation change and the distance traveled along the road are known. This requires the use of trigonometry to determine the angle, given the rise (elevation change) and run (distance traveled along the road).

To find the angle, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle. In this scenario, the rise is 160 m and the run is 2400 m (2.4 km). We need to convert the run into meters to match the units of the rise, making the run 2400 m.

Now we compute the angle θ:

• Rise (opposite side) = 160 m
• Run (adjacent side) = 2400 m
• Tangent of θ = Rise / Run = 160m / 2400m
• Tan θ = 1/15
• θ = arctan(1/15)

Once we calculate the arctan(1/15), we will get the angle of inclination of the road in degrees.

Answer 2

The 'slope' of the road is (rise between two points) / (hotizontal distance between the same two points). Or (rise)/(run). It's also the tangent of the angle between the horizontal and the incline.

In this problem, your 'run' is 2.4 km, and the 'rise' is 160 m.

The slope of the incline is (160) / (2,400) .

That's 0.0667 .

To answer the question, you need to find the ANGLE whose tangent is that same number.

If your calculator has ANY functions on it, then " tan⁻¹ " is the one you want. Key in a number, and " tan⁻¹ " will give you the angle whose tangent is that number.