AB is a vertical pole resting at the end A on the level ground. P is a point on the level ground such that AP = 3AB and C Is the midpoint of AB. If AC and CB subtend angles `alpha` and `beta`, respectively, at P, then the value of tan`beta` is

Options

A. `(18)/(19)`
B. `3/19`
C. `1/6`
D. `1/3`

Explanation

To solve the problem step by step, let's denote the height of the vertical pole AB as \( AB = h \).

### Step 1: Define the lengths
Let \( AB = h \). Since \( C \) is the midpoint of \( AB \), we have:
- \( AC = \frac{h}{2} \)
- \( CB = \frac{h}{2} \)

Given that \( AP = 3AB \), we can write:
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