Question

1. the slope distance between two points is 21.835 m and the difference in elevation between the points is 3.658 m. compute the horizontal dist

Explanation:

Step1: Apply Pythagorean theorem

Let the slope - distance be $l = 21.835$ m, the elevation difference be $h=3.658$ m, and the horizontal distance be $x$. According to the Pythagorean theorem $l^{2}=x^{2}+h^{2}$, so $x=\sqrt{l^{2}-h^{2}}$.

Step2: Substitute values

Substitute $l = 21.835$ and $h = 3.658$ into the formula: $x=\sqrt{(21.835)^{2}-(3.658)^{2}}=\sqrt{476.779 - 13.381}=\sqrt{463.398}$.

Step3: Calculate the result

$x\approx21.527$ m.

Answer:

$21.527$ m