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A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west corner, she measures the first side to be 80 m long and the next to be 105 m -- these sides are represented as displacement vectors A and B in Figure 3.26, where θ1=19°, and θ2=12°. She then correctly calculates the length and orientation of the third side C. What is her result?

Find the magnitude and the direction south of west

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A) Y = 80 * SIN 19 = - 26.045

A) X = 80 * COS 19 = 75.64

B) Y = 105 * COS 12 = 102.71

B) X = 105 * SIN 12 = -21.831

TOTAL Y = 102.71 - 26.045 = +76.67

TOTAL X = 75.64 - 21.831 = +53.81

Third Side : C) = SQRT (76.67.^2 + 53.81^2) = 93.69 Meters length

Third Side : C) Angle = ARC TAN 76.67 / 53.81 = 54.97 degrees North of Due West

from the West Corner

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