A shoreline observation post is located on a cliff such that the observer is 280 feet above sea level. The observer spots a ship approaching the shore and the ship is traveling at a constant speed.

Requried:
a. When the observer initially spots the ship, the angle of depression for the observer's vision is 6 degrees. At this point in time, how far is the ship from the shore?
b. After watching the ship for 43 seconds, the angle of depression for the observer's vision is 16 degrees. At this point in time, how far is the ship from the shore?

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Answer :

JOAOBEZERRAGO JOAOBEZERRAGO · Answer 1

Using the slope concept, it is found that the distances from the shore at each moment are given by:

a) 2664 feet.

b) 976 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

Item a:

The vertical distance is of 280 feet, with an angle of 6º. The distance from the shore is the horizontal distance of x. Hence:

[tex]\tan{6^\circ} = \frac{280}{x}[/tex]

[tex]x = \frac{280}{\tan{6^\circ}}[/tex]

x = 2664.

Item b:

The vertical distance is of 280 feet, with an angle of 16º. The distance from the shore is the horizontal distance of x. Hence:

[tex]\tan{16^\circ} = \frac{280}{x}[/tex]

[tex]x = \frac{280}{\tan{16^\circ}}[/tex]

x = 976.

More can be learned about the slope concept at https://brainly.com/question/18090623