# A farmer wants to wall off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, where A = 4.99 km, B = 2.46 km, and C = 3.23 km and then correctly calculates the length and orientation of D?

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A farmer wants to wall off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, where A = 4.99 km, B = 2.46 km, and C = 3.23 km and then correctly calculates the length and orientation of the fourth side D.

A: What is the length of the vector D in kilometers?

B: What is the orientation of the vector D, in degrees W of S?

A farmer wants to wall off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, where A = 4.99 km, B = 2.46 km, and C = 3.23 km and then correctly calculates the length and orientation of the fourth side D.

A: What is the length of the vector D in kilometers?

B: What is the orientation of the vector D, in degrees W of S?

##### 1 Answer

#### Answer:

**Magnitude**:

**Orientation**:

#### Explanation:

**Polar Representation**:

All angles must be measured counter-clockwise from the positive direction of the X-axis (usually East)

**Cartesian Representation**:

**Zero Displacement Condition**:

**Magnitude**:

**Orientation**:

**Note**: In calculating the orientation, we recognize that the vector lies in the third quadrant because both the X and Y component are negative. Since the '