Question

compute the corrected horizontal distance under the following conditions (assume normal tension was used).
temperature: 0 °c
tape length: 30.002 m
slope angle: 1.5°
slope measurement: 225.000 m

Explanation:

Step1: Convert slope percentage to angle

The slope percentage is 1.5%. The slope angle $\theta$ in radians can be found from the formula $\tan\theta=\frac{1.5}{100}$. So, $\theta = \arctan(0.015)$.

Step2: Use slope - distance correction formula

The formula for correcting a sloped distance $L$ to a horizontal distance $D$ is $D = L\cos\theta$. Given $L = 225.000$ m. First, calculate $\cos\theta=\cos(\arctan(0.015))$. Since $\tan\theta = 0.015=\frac{y}{x}$, using the Pythagorean theorem $r=\sqrt{x^{2}+y^{2}}=\sqrt{1 + 0.015^{2}}$, and $\cos\theta=\frac{1}{\sqrt{1+0.015^{2}}}$. Then $D = 225\times\frac{1}{\sqrt{1 + 0.015^{2}}}$.
$D=225\times\frac{1}{\sqrt{1+0.000225}}=225\times\frac{1}{\sqrt{1.000225}}\approx225\times0.999887 = 224.974$ m

Answer:

224.974 m