The upper `3/4` th portion of a vertical pole subtends an angle `theta` such that tan `theta=3/5` at a point in the horizontal plane through its foot and at a distance 40m from the foot. Find the possible height of the vertical pole.

Explanation

To solve the problem step by step, we will follow the given information and use trigonometric identities.

### Step 1: Define the variables
Let the total height of the pole be \( h \). The upper \( \frac{3}{4} \) portion of the pole is \( \frac{3}{4}h \). The distance from the foot of the pole to the point where the angle is measured is \( 40 \) meters.

### Step 2: Use the tangent of the angle
We are given that \( \tan \theta = \frac{3}{5} \). This means that at the point where the angle is measured, the opposite side (the height of the upper \( \frac{3}{4} \) of the pole) and the adjacent side (the distance from the pole) can be represented as:
\[
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