Calculate Staff Intercept (s)

The staff intercept $s$ is the difference between the top reading and the bottom reading on the staff.

$s = 3.0\text{ m} - 1.0\text{ m} = 2.0\text{ m}$

State Tacheometric Distance Formula

For an inclined line of sight, the formula for horizontal distance $D$ is given by:

$D = k \cdot s \cdot \cos^2\theta + c \cdot \cos\theta$

Substitute Given Values

Substitute $k = 100$, $s = 2.0\text{ m}$, $\theta = -5°$, and $c = 0$ into the formula. Note that $\cos(-5°) = \cos(5°)$.

$D = 100 \times 2.0 \times \cos^2(5°) + 0$

Calculate Horizontal Distance

Since $\cos(5°) \approx 0.9961947$, calculate the squared cosine and multiply by $200$.

$D = 200 \times (0.9961947)^2 = 200 \times 0.99240387 = 198.48076\text{ m}$