Question

a man lying down on a top of a cliff 40m observes angle of depression of a buoy to be 20° if he is in line with the buoy calculate distance between buoy and the feet of the cliff (which may be assumed to be vertical) ​

Answer 1

Answer: 109.89 m

Step-by-step explanation:

In order to solve this problem, the figure attached will be helpful.

As we can see, the angle of depression (below the horizontal line) is
`20\º`, if we know the angle between the horizontal and the ground (bottom of the cliff) is
`90\º`, by simple geometry we will know the other angle is
`70\º`:

`90\º=70\º+20\º`

Now, we have a right triangle here and we need to find
`X` which is istance between buoy and the feet of the cliff, and we can solve this by using the tangent trigonometric function:

`tan\theta=(Oppositeside)/(Adjacentside)` (1)

Where:

`\theta=70\º`

`Oppositeside=X`

`{Adjacentside=40m`

Rewritting equation (1):

`tan(70\º)=(X)/(40m)` (2)

Finding
`X`:

`X=(40m)(tan(70\º))` (3)

`X=109.89m` >>>distance between buoy and the cliff