# A store wants to mount a security camera to record video of the door and the cash register. The best non-moving camera will covera specific angle of up ............. to 180 degree. The caera will...

A store wants to mount a security camera to record video of the door and the cash register. The best non-moving camera will covera specific angle of up ......

....... to 180 degree. The caera will be mounted 30 Ft from the door and 20  Ft from the cash register. If the door is 15 Ft from the cash register, what angle must the camera cover to watch both sites? Include a diagram.

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should use the following notations: camera = C, door = D, cash register = E.

If you link these 3 points, you'll form a triangle. The lengths of the sides of triangle are CD = 30 ft ; CE = 20 ft ; DE = 15 ft.

You need to find the angle comprised between CD and CE.

You should use the law of cosines such that:

`cos alpha = (CD^2 + CE^2 - DE^2)/(2*CD*CE)` `cos alpha = (30^2 + 20^2 - 15^2)/(2*30*20)`

`cos alpha = (900 +400 - 225)/(2*30*20)`

`cos alpha = 1075/1200 =gt cos alpha = 0.895`

`` `alpha = 26.4^o`

The angle camera should cover is of `26.4^o` .