A ladder rest against a wall making an angle `alpha` with the horizontal. The foot of the ladder is pulled away from the wall through a distance `x ,` so that it slides a distance `y` down the wall making an angle `beta` with the horizontal. THEN x=

Options

A. `y= xtan""(alpha+beta)/2`
B. `x= ytan""(alpha+beta)/2`
C. `x= ytan""(alpha+beta)`
D. `y= xtan""(alpha+beta)`

Explanation

To solve the problem step by step, we will analyze the situation involving the ladder, the wall, and the angles involved.

### Step 1: Understand the Setup
We have a ladder resting against a wall, forming an angle \( \alpha \) with the horizontal. The foot of the ladder is pulled away from the wall by a distance \( x \), and as a result, the top of the ladder slides down the wall by a distance \( y \), forming a new angle \( \beta \) with the horizontal.

### Step 2: Define the Length of the Ladder
Let the length of the ladder be \( L \). Since the length of the ladder remains constant, we can express it in terms of the distances involved:
- Initially, when the ladder makes an angle \( \alpha \):
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