To find the height of the tower, we need to use trigonometric concepts related to angles of elevation. Let's denote the following:

• \(h\): Height of the tower.
• \(x\): Initial distance from the tower.
• \(\theta_1\): Initial angle of elevation where \(\tan \theta_1 = \frac{5}{6}\).
• \(\theta_2\): Angle of elevation after moving 70 meters closer, where \(\tan \theta_2 = \frac{9}{2}\).

Initially, the tangent of the angle of elevation is the ratio of the opposite side (height of the tower) to the adjacent side (distance \(x\)):

\(\tan \theta_1 = \frac{h}{x} = \frac{5}{6}\).

From this, we have:

\(h = \frac{5}{6}x\) (Equation 1).

After moving 70 meters towards the tower, the tangent of the new angle of elevation is:

\(\tan \theta_2 = \frac{h}{x - 70} = \frac{9}{2}\).

From this, we have:

\(h = \frac{9}{2}(x - 70)\) (Equation 2).

Equate Equation 1 and Equation 2 to solve for \(x\):

\(\frac{5}{6}x = \frac{9}{2}(x - 70)\).

Solving the equation:

1. Cross Multiply: \(5(x - 70) = 27x\).
2. Expand: \(5x - 350 = 27x\).
3. Rearrange terms to solve for \(x\): \(350 = 27x - 5x\).
4. Simplify: \(22x = 350\).
5. Calculate \(x\): \(x = \frac{350}{22} = \frac{175}{11}\) (m).

Substitute \(x\) back into Equation 1 to find \(h\):

\(h = \frac{5}{6} \times \frac{175}{11}\).

Calculate \(h\):

\(h = \frac{875}{66} \approx 225 \text{ m}\).

Therefore, the height of the tower is 225 meters.