A 1.6 km road rises 400 m. What is the angle of elevation of the road to the nearest degree?
rise/run
= 400/1600
= 1/4
= tan Ø
Ø = appr 14°
To find the angle of elevation, we can use the tangent function.
Tangent(angle) = Opposite/Adjacent
In this case, the Opposite side is the height of the road, which is 400 m, and the Adjacent side is the horizontal distance of the road, which is 1.6 km or 1600 m.
Tangent(angle) = 400/1600
Now, let's calculate the tangent(angle):
Tangent(angle) = 400/1600
Tangent(angle) = 0.25
To find the angle, we need to inverse the tangent function. We can use a scientific calculator or an online trigonometry calculator for this.
So, the angle of elevation of the road is approximately 14 degrees to the nearest degree.
To find the angle of elevation, you need to use trigonometry. The angle of elevation is the angle formed between the horizontal line and your line of sight to the object you are observing, in this case, the road.
Let's call the angle of elevation θ. We can use the tangent function in trigonometry to find θ.
Tangent (θ) = Opposite / Adjacent.
In this case, the opposite side is the rise of the road, which is 400 meters, and the adjacent side is the horizontal distance of the road, which is 1.6 kilometers or 1600 meters.
Tangent (θ) = 400 / 1600.
Simplifying this equation gives:
Tangent (θ) = 0.25.
Now, to find the angle θ, we need to take the arctangent (inverse tangent) of both sides of the equation.
θ = arctan(0.25).
Using a calculator or a table of trigonometric values, you can find that the arctangent of 0.25 is approximately 14.0 degrees.
Therefore, the angle of elevation of the road is approximately 14 degrees to the nearest degree.