Question

A pilot 4220 m directly above the front of a straight train observes that the angle of
depression to the end of the train is 68.2 degree. Find the length of the train.

Answer 1

Answer:

1688 m

Step-by-step explanation:

plz refer the picture

Answer 2

The length of the train is 1687.8 meters.

Given:

The height at which the pilot is present exactly above the front of a straight train when he saw the train is (h) = 4220 m.

The angle of depression to the end of the train is (∅) = 68.2°.

To Find:

The length of the train (l) =?

Solution:

Here, we will use the basic trigonometric formula to calculate the length of the train.

i.e., we will be using the 'tan' of angle formula;

i.e.,  tan∅ = $\frac{Opposite Side}{Adjacent Side}$

We have given the angle of depression to the end of the train as follows;

i.e., ∅ = 68.2°.

The approximate diagram is shown in the figure below;

where the angle of depression = ∠B

∴ tan(B) = tan∅ = $\frac{AC}{BC}$

∴ tan( 68.2° ) =  $\frac{4220}{l}$

∴ 2.5 =   $\frac{4220}{l}$

∴ l  = $\frac{4220}{2.5}$

∴ l = 1688 meters approximately.

Therefore, the actual length of the train is found to be 1687.8 m.

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