Question

compute the corrected horizontal distance under the following conditions (assume normal tension was used). temperature: 46 °f tape length: 100.00 ft slope angle: 3° 18 slope measurement: 219.51 ft

Explanation:

Step1: Convert angle to decimal degrees

The slope - angle is $3^{\circ}18'$. We know that $18'=\frac{18}{60}=0.3^{\circ}$, so the angle $\theta = 3 + 0.3=3.3^{\circ}$.

Step2: Use the formula for horizontal distance

The formula for the horizontal distance $D$ given the slope - distance $L$ and slope - angle $\theta$ is $D = L\cos\theta$. Here, $L = 219.51$ ft and $\theta = 3.3^{\circ}$.
We know that $\cos(3.3^{\circ})\approx0.9984$.
So, $D = 219.51\times0.9984\approx219.16$ ft.

Answer:

$219.16$ ft