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

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:

$tan\theta=\frac{Oppositeside}{Adjacentside}$   (1)

Where:

$\theta=70\º$

$Oppositeside=X$

${Adjacentside=40m$

Rewritting equation (1):

$tan(70\º)=\frac{X}{40m}$   (2)

Finding $X$:

$X=(40m)(tan(70\º))$   (3)

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