Question

What is the angle of depression from micheal to the plate?

Answer 1

First let's start by drawing the described problem so we can better understand the procedure to follow:

In the above representation, we can see that the height of the given triangle can be determined by subtracting the height of the table from Michael's height, like this:

h = 5.6 - 2 = 3.6

Then, the triangle has the following dimensions:

As you can see, we have a right triangle, by taking the tangent of the angle θ, we get the following expression:

`tan(θ)=(ol)/(al)`

Where ol is the opposite leg to the angle θ and al is the adjacent leg to this angle, in this case, ol is 11 and al is 3.6, then we get:

`tan(θ)=(11)/(3.6)`

By taking the inverse tangent function, we get:

`\begin{gathered} tan^(-1)(tan(θ))=tan^(-1)((11)/(3.6)) \\ θ=72 \end{gathered}`

Then, the angle of depression is 72 degrees