Question

Question #8fa79

Answer 1

`(BG)/(AG), (CF)/(AF) and (DE)/(AE)`

Explanation:

So the formal definition of the tangent is:
`tan theta=sin theta/cos theta`

Now, when dealing with right triangles, the sine is:
`sin theta="opposite"/"hypotenuse"`

and the cosine is:
`cos theta="adjacent"/"hypotenuse"`

putting both together gets us:
`tan theta=("opposite"/"hypotenuse")/("adjacent"/"hypotenuse")`

`tan theta="opposite"/"hypotenuse"*"hypotenuse"/"adjacent"`

The hypotenuses cancel out leaving us with:
`tan theta="opposite"/"adjacent"larr` this is the tangent ratio

So, looking at the picture the ratios are:
`(BG)/(AG), (CF)/(AF) and (DE)/(AE)`