From the data provided above, we know that the vertical displacement is 17.63 meters and the horizontal displacement is 100 meters. Assuming the path taken is a straight line, this forms a right angle triangle, with the vertical displacement and horizontal displacement as the two shorter sides, or the legs.
We can find the slope of this triangle - and hence, the road - by dividing the vertical displacement with the horizontal displacement. This calculation is based on a basic trigonometric principle from the mnemonic SOH-CAH-TOA, where TOA stands for Tangent of an angle equals Opposite side divided by Adjacent side.
Here, our "opposite" side is the vertical displacement while our "adjacent" side is the horizontal displacement. Therefore, we compute:
slope = vertical displacement / horizontal displacement
= 17.63 / 100
= 0.1763
Now, this is the slope of the road or in trigonometric terms, the tangent of the angle of inclination. To find the angle itself, we have to find the arctangent or the inverse of the tangent function.
Before proceeding, please note that commonly used scientific calculators or programming languages will return this value in radians, which is a unit of angle measurement. Since we commonly use degrees to measure angles, we have to convert this value from radians to degrees.
Let's find the angle α:
α = arctangent(slope)
= arctangent(0.1763) // calculation in radians
= 9.9985 degrees // after conversion from radians to degrees
Therefore, the road's approximate angle of inclination is
Answer: 9.9985 degrees.