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 feet.

460 ft.

Step-by-step explanation:

Please find the attachment.

Let h be the vertical height that train climbed.

We have been given that a train traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of 5°. We are asked to find the vertical height that train climbed.

We can see from our attachment that the distance traveled by train and hill forms a right triangle with respect to ground, where 5280 is hypotenuse to the 5 degree angle.

We know that sine relates the opposite side of a right triangle with hypotenuse, so we can set an equation as:

Therefore, the train climbed approximately 460 feet.

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step-by-step explanation: