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
$\bigcirc$ $\frac{bd}{ed}$ $\bigcirc$ $\frac{ed}{dc}$
$\bigcirc$ $\frac{db}{dc}$ $\bigcirc$ $\frac{bd}{eb}$

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
$\bigcirc$ $\frac{bd}{ed}$  $\bigcirc$ $\frac{ed}{dc}$
$\bigcirc$ $\frac{db}{dc}$  $\bigcirc$ $\frac{bd}{eb}$

Accepted Answer

# Answer:
$\frac{DB}{EB}$

# Explanation:
## Step1: Define tan E in △EDC
$	an E = \frac{	ext{opposite}}{	ext{adjacent}} = \frac{DC}{ED}$

## Step2: Identify similar triangles
△EDB ~ △ECD (AA similarity: ∠E common, right angles)

## Step3: Set up ratio from similarity
$\frac{DB}{DC} = \frac{EB}{ED} \implies \frac{DB}{EB} = \frac{DC}{ED}$

## Step4: Equate to tan E
$	an E = \frac{DC}{ED} = \frac{DB}{EB}$

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