could you please show full eorking cos i have my finals on it. incase the questi

Question

could you please show full eorking cos i have my finals on it. incase the questiom is not seen, this is the question "A water is to be constructed with a 19% grade in the north direction and a 18% grade in the east direction. Determine the angke theta required in the water main for the turn from north to east. theta= "

MAA MATHEMATICAL ASSOCATION HwT 11.3 v2: Problem 4 pt A water main is to be constructed with a 19% gade in the aorth dnection and 18s grade the east dwarsen Determine the agedieorindin the wND nan la north to east. You have attempted this problem 4 tim Your overal tecorded score 0% You have unlimited amempts rem

Explanation / Answer

Solution:

Let
y = north direction
x = east direction
z = vertical

(x, y, z) = (east, north, vertical)

The unit vectors in the two directions are;

The first direction (north) is represented by the vector

N: (0, 1, .19)/sqrt(1.0361)

The second direction (east) is represented by the vector

E: (1, 0, .18)/sqrt(1.0324)

Take the dot product

N dot E = cos(theta) = (0.19)*(0.18)/sqrt(1.0361*1.0324) = .0342/sqrt(1.0696) = 0.033

cos(theta) = 0.033
theta = 88.10 degrees.

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