Question

A train 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.

Answer 1

Use the sin ratio to solve for this. We are looking for the height which, in a right triangle, would be the side opposite the reference angle, and the hypotenuse. The ratio would look like this: sin(5) = x/5280. Multiply both sides by 5280 to get 5280 sin(5) = x and x = 460.18 ft

Answer 2

460 ft.

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:

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{sin}(5^(\circ))=\frac{\text{h}}{5280}`

`0.087155742748=\frac{\text{h}}{5280}`

`0.087155742748*5280=\frac{\text{h}}{5280}*5280`

`460.18232=h`

`h\approx 460`

Therefore, the train climbed approximately 460 feet.