5) A truck drives 15.9 km up a road, until it has gone 2.1 km vertically. If the road has a steady incline, what is the angle of elevation of the road?
I believe that should be
sin(Θ) = 2.1 / 15.9
tan(Θ) = 2.1 / 15.9
oobleck is correct
To find the angle of elevation of the road, we can use the trigonometric relationship involving the vertical and horizontal distances traveled. The tangent of the angle of elevation can be determined by dividing the vertical distance by the horizontal distance.
In this case, the vertical distance is given as 2.1 km, and the horizontal distance is given as 15.9 km. Therefore, we can calculate the tangent of the angle of elevation as follows:
tangent of angle of elevation = vertical distance / horizontal distance
tangent of angle of elevation = 2.1 km / 15.9 km
Now, let's calculate the tangent of the angle of elevation:
tangent of angle of elevation ≈ 0.1321
To find the angle of elevation, we need to take the inverse tangent (arctan) of the result. Using a calculator or a mathematical function, we can find the angle of elevation:
angle of elevation ≈ arctan(0.1321) ≈ 7.52 degrees
Therefore, the angle of elevation of the road is approximately 7.52 degrees.