Question

A security light is being installed outside a loading dock. The light is mounted 20feet above the ground. The light must be placed in an angle so that it will illuminate the end of the parking lot. If the end of the parking lot is 100 feet from the loading dock, what should be the angle of depression of the light

Answer 1

check the picture below.

make sure your calculator is in Degree mode.

Answer 2

`11.31^(\circ)`

Explanation:

Let x represent angle of depression.

We have been given that a security light is being installed outside a loading dock. The light is mounted 20 feet above the ground. The end of the parking lot is 100 feet from the loading dock.

We can see that security light, parking lot and angle of depression forms a right triangle with respect to ground. The side that is 20 ft is the opposite side and side 100 ft is adjacent to angle of depression.

`\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

`\text{tan}(x)=(20)/(100)`

`\text{tan}(x)=0.2`

Now, we will use inverse tangent or arctan to solve for x.

`x=\text{tan}^(-1)(0.2)`

`x=11.30993247^(\circ)`

`x\approx 11.31^(\circ)`

Therefore, the angle of the depression of the light is approximately 11.31 degrees.