Atrain traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of 5°. the vertical height that the train climbed is approximately _ ft?

You can draw a right triangle where>

1) the distance traveled, i.e. 5280, is the hypotenuse

2) the opposite-leg is the vertical height that you need to calculate

3) the angle is 5°.

Therefore you can use the trigonometric ratio sine, which is:

sin(angle) = opposite-leg / hypotenuse = vertical height / distance traveled

= vertical height = distance traveled * sin (angle)

=> vertical height = 5,280 ft * sin(5°) = 460,18 ft

460,18 ft