Katoomba scenic railway in Australia is the steepest railway in the world. The railway makes an angle of 52 degrees with the ground. The railway extends horizontally about 458 ft. What is the height of the railway?
here hope this helps
Let the horizontal distance = x = 458 feet
And the vertical distance which is the height = y
The railway makes an angle of about 52º with the ground.
∴ y = x tan 52° = 458 * tan 52° = 586.21 feet ≈ 586 feet
The height of the railway is 586 feet
To find the height of the railway, we can use the trigonometric function tangent. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the angle is 52 degrees and the adjacent side is 458 ft (the horizontal length of the railway). Let's call the height of the railway "h".
The tangent of 52 degrees is equal to the height divided by the adjacent side:
tan(52) = h / 458
To find the height, we can rearrange the equation:
h = tan(52) * 458
Using a calculator, we can evaluate the equation:
h ≈ 1.2793 * 458
h ≈ 586.72 ft
Therefore, the height of the railway is approximately 586.72 ft.
To find the height of the railway, we can use trigonometry. The angle of 52 degrees is the angle between the railway and the horizontal ground.
Let's label the height of the railway as 'h' and the horizontal distance as 'd'. In this case, 'd' is given as 458 ft.
Using trigonometry, we know that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the railway (h) and the adjacent side is the horizontal distance (d).
So, we can write:
tan(52 degrees) = h / d
Substituting the values, we get:
tan(52 degrees) = h / 458
Now, we need to find the value of h. To do that, rearrange the equation:
h = tan(52 degrees) * 458
Now, let's calculate it using a calculator:
h ≈ tan(52 degrees) * 458
h ≈ 1.275 * 458
h ≈ 584.45 ft
Therefore, the height of the Katoomba scenic railway in Australia is approximately 584.45 ft.