A security camera at a local bank is mounted on a wall 11 feet above the floor. What angle of depressions should be used if the camera is to be directed on a spot 6 feet above the floor and 29 feet away from the wall?

What is the angle of depression?

Question

A security camera at a local bank is mounted on a wall 11 feet above the floor. What angle of depressions should be used if the camera is to be directed on a spot 6 feet above the floor and 29 feet away from the wall? 

What is the angle of depression?

mathstudent55 · Answer

You are looking for x.

|dw:1392791736515:dw|

mathstudent55 · Answer

Find y using trig. Then subtract y from 90 deg to find x.
|dw:1392791912626:dw|

awy · Answer

oh i see, i drew the triangle wrong....

awy · Answer

x=9.782 degrees

awy · Answer

wait, you mean find x using trig? i dont see y

awy · Answer

oh nvm

awy · Answer

y=69.228 degree

awy · Answer

so 90 - 69.228 = 20.772 degrees

anonymous · Answer

Sorry, I posted y.  x is the angle of depression.

mathstudent55 · Answer

You need to be careful with the picture.
I realize the picture is a little confusing because of the 11 ft and the 5 ft lengths.

The triangle you need to deal with is the triangle shown in black in the figure below.
For that triangle, the opposite side to angle y has a length of 29 ft. The adjacent side to angle y has a length of 5 ft, not 11 ft.

To find y, you need the inverse tangent, as you did, but the correct lengths are:

$\tan^{-1} \dfrac{29}{5} $

Once you find y, then you can find x as you did.

|dw:1392855120872:dw|