A vertical pole with height more than 100 m consists of two parts, the lower being one-third of the whole. At a point on a horizontal plane through the foot and 40 m from it,the upper part subtends an angle whose tangent is `1/2` What is the height of the pole

Explanation

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

### Step 1: Determine the height of the lower and upper parts of the pole
The height of the pole consists of two parts:
- The lower part is one-third of the whole height, which is \( \frac{h}{3} \).
- The upper part is the remaining two-thirds, which is \( \frac{2h}{3} \).

### Step 2: Set up the tangent relationship
...