If the intercept on a vertical staff is ob-served as 0.75 m from a tacheometer, the horizontal distance between tacheometer and staff station is A. 7.5 m B. 25 m C. 50 m D. 75 m

The correct answer is $\boxed{\text{B. }25\text{ m}}$.

The horizontal distance between the tacheometer and the staff station is equal to the tangent of the angle of elevation times the intercept on the staff. In this case, the angle of elevation is 45 degrees, and the intercept on the staff is 0.75 m. Therefore, the horizontal distance is $0.75 \times \tan(45^\circ) = 25\text{ m}$.

Option A is incorrect because it is the square of the correct answer. Option C is incorrect because it is the square root of the correct answer. Option D is incorrect because it is the product of the correct answer and the sine of the angle of elevation.