Please answer the following question(s): 1. C= y e= A+B+C =0 Ꮎ = ? C = ? m m 21° A = 80 m B = 105 m B 11° I 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 from B in the figure above. She then correctly calculates the length and the compass direction of the third side C. What is her result? S degrees south of west - E

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Chapter1: Units, Trigonometry. And Vectors
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Please answer the following question(s):

1. 

The diagram shows a triangle with its sides labeled as vectors \( \mathbf{A} \), \( \mathbf{B} \), and \( \mathbf{C} \) forming a closed loop, satisfying the equation \( \mathbf{A} + \mathbf{B} + \mathbf{C} = 0 \).

- Vector \( \mathbf{A} \) is 80 meters long at an angle of 21° south of the west.
- Vector \( \mathbf{B} \) is 105 meters long at 11° north of the east.

The objective is to find:
- The magnitude of vector \( \mathbf{C} \).
- The direction \( \theta \) (compass direction) of vector \( \mathbf{C} \), measured in degrees south of west.

Text description below:

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 the figure above. She then correctly calculates the length and the compass direction of the third side \( C \). What is her result?

Boxes for the answers:

\( C = \) [Box for answer] m  
\( \theta = \) [Box for answer] degrees south of west

A compass rose in the diagram indicates the cardinal directions: North (N), East (E), South (S), and West (W).
Transcribed Image Text:Please answer the following question(s): 1. The diagram shows a triangle with its sides labeled as vectors \( \mathbf{A} \), \( \mathbf{B} \), and \( \mathbf{C} \) forming a closed loop, satisfying the equation \( \mathbf{A} + \mathbf{B} + \mathbf{C} = 0 \). - Vector \( \mathbf{A} \) is 80 meters long at an angle of 21° south of the west. - Vector \( \mathbf{B} \) is 105 meters long at 11° north of the east. The objective is to find: - The magnitude of vector \( \mathbf{C} \). - The direction \( \theta \) (compass direction) of vector \( \mathbf{C} \), measured in degrees south of west. Text description below: 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 the figure above. She then correctly calculates the length and the compass direction of the third side \( C \). What is her result? Boxes for the answers: \( C = \) [Box for answer] m \( \theta = \) [Box for answer] degrees south of west A compass rose in the diagram indicates the cardinal directions: North (N), East (E), South (S), and West (W).
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