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A mountain railway AB is of length 864m and rises at an angle of 120° to the horizontal.

A train is 856m above sea level when it is at A.
calculate the height above sea level of the train when it reaches B​.​

User Karthick Selvaraj
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1 Answer

15 votes
15 votes

Answer:

The height above sea level at B is approximately 1,604.25 m

Explanation:

The given length of the mountain railway, AB = 864 m

The angle at which the railway rises to the horizontal, θ = 120°

The elevation of the train above sea level at A, h₁ = 856 m

The height above sea level of the train when it reaches B, h₂, is found as follows;

Change in height across the railway, Δh = AB × sin(θ)

∴ Δh = 864 m × sin(120°) ≈ 748.25 m

Δh = h₂ - h₁

h₂ = Δh + h₁

∴ h₂ ≈ 856 m + 748.25 m = 1,604.25 m

The height above sea level of the train when it reaches B ≈ 1,604.25 m

User Thomasbabuj
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