Question

question
in the diagram of right triangle edc below, altitude \\(\overline{db}\\) is drawn. which of the following ratios is equivalent to \\(\tan e\\)?
diagram of right triangle edc with altitude db
answer
\\(\frac{bd}{ed}\\) \\(\frac{ed}{dc}\\)
\\(\frac{db}{dc}\\) \\(\frac{bd}{eb}\\)

Explanation:

Step1: Define $\tan E$ in $\triangle EDC$

$\tan E = \frac{\text{opposite}}{\text{adjacent}} = \frac{DC}{ED}$

Step2: Use similar triangles

$\triangle EBD \sim \triangle EDC$, so $\tan E = \frac{DB}{EB}$

Step3: Match with options

Identify the equivalent ratio from the choices.

Answer:

$\frac{DB}{EB}$ (assuming this is one of the options; if the correct option is, e.g., $\frac{DC}{ED}$, adjust accordingly—note: based on standard right triangle altitude properties, $\tan E = \frac{DC}{ED} = \frac{DB}{EB}$)