A ship is 7 ft from the dock. One sailor who is standing at the front of the boat 10 ft above dock level tosses rope to another sailor who is standing on the dock to tie the boat to the dock. How is the angle of elevation for the sailor standing on the dock related to the angle of depression for the sailor standing at the front of the boat?

The angle of elevation for the sailor standing on the dock is equal to the angle of depression for the sailor standing at the front of the boat which is 55 degrees.

What is angle of elevation?

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

What is angle of depression?

The angle of depression is the angle between the horizontal line and the line of sight which is below the horizontal line.

Given information-

The distance between the ship and dock is 7 ft.

The one sailor is standing 10 ft above the dock level.

The another sailor is standing on the dock.

The angle of depression and elevation is shown in the image.

Here the angle made by the sailor who is 10 ft above from the dock level on the ship is,

[tex]\tan \theta=\dfrac{10}{7}[/tex]

Find the value of angle as,

[tex]\theta=\tan ^-(\dfrac{10}{7})\\\theta=55[/tex]

Hence the angle of depression is 55 degree.

As the angle of the depression is equal to the angle of depression for the same place.

Thus the angle of elevation is 55 degrees.

Hence, The angle of elevation for the sailor standing on the dock is equal to the angle of depression for the sailor standing at the front of the boat which is 55 degrees.

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