Question

the slope measurement between two points is 36.255 m, and the slope angle is 1°50. compute the horizontal distance.

Explanation:

Step1: Convert angle to decimal degrees

First, convert $1^{\circ}50'$ to decimal degrees. Since $1^{\circ}=60'$, then $50'=\frac{50}{60}\approx0.8333^{\circ}$. So the angle $\theta = 1 + 0.8333=1.8333^{\circ}$.

Step2: Use cosine - relation

We know that $\cos\theta=\frac{\text{horizontal distance}}{\text{slope distance}}$. Let the horizontal distance be $x$ and the slope distance $d = 36.255$ m and $\theta=1.8333^{\circ}$. Then $x = d\cos\theta$.
$x=36.255\times\cos(1.8333^{\circ})$
Since $\cos(1.8333^{\circ})\approx0.9995$, then $x = 36.255\times0.9995\approx36.247$ m.

Answer:

$36.247$ m