Question

Juliet stands at the window of her apartment so that her eyes are 38.4 feet above the ground. Juliet spots her boyfriend down the street a few blocks away. She knows, based off the number of city block, that her boyfriend is at a distance of 156.45 feet away from the building. Determine the angle of depression of juliet’s site to her boyfriend on the ground

Answer 1

Answer: $13.79\º$  

The angle of depression is that which measurement is made between the visual line and the horizontal line (figure attached), taking into account that the object that forms the angle is below the horizontal.

In additon, this angle is congruent with the elevation angle.

In the attached figure we can see the situation described in the statement:

The figure formed is a right triangle with two known sides. We can use the tangent trigonometric function to find the value of the angle $\theta$, as follows:

$tan(\theta)=\frac{OC}{AC}$  

Where $OC=38.4ft$ is the opposite cathetum or leg to the angle $\theta$, and  $AC=156.45ft$ is the adjacent cathetum or leg to $\theta$.

Then:

$tan(\theta)=\frac{38.4}{156.45ft}$  

$tan(\theta)=0.245$  

$\theta=arctan(0.245)$  

Finally we find the angle of depression of Juliet’s site to her boyfriend on the ground:

$\theta=13.79\º$