Finding the resultant of two vectors

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SUMMARY

The discussion focuses on calculating the resultant of two vectors, S and T, using their rectangular components. Vector S has a magnitude of 24.3 units at an angle of 54.8 degrees below the negative x-axis, while vector T has a magnitude of 18.8 units at an angle of 37.7 degrees above the positive x-axis. Participants emphasize the importance of resolving each vector into its x and y components using sine and cosine functions, and they highlight the use of tangent to determine unknown angles in right triangles formed by the vectors.

PREREQUISITES
  • Understanding of vector resolution into components
  • Knowledge of trigonometric functions: sine, cosine, and tangent
  • Familiarity with angles and their relationships in right triangles
  • Ability to perform vector addition
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  • Practice resolving vectors into rectangular components using different magnitudes and angles
  • Learn about vector addition in two dimensions
  • Explore the concept of complementary angles in right triangles
  • Study the application of trigonometric identities in vector problems
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Students studying physics or mathematics, particularly those focusing on vector analysis and trigonometry.

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Homework Statement


S is a vector 24.3 units in magnitude and points at an angle of 54.8 degrees below the negative x-axis. T is a vector 18.8 units in magnitude and points at an angle of 37.7 degrees above the positive x axis. Find the resultant of the two vectors by resolving into rectangular components.

Homework Equations


The Attempt at a Solution

 
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Sketch right triangles involving S and T and use cosine and sine to find each vector's x and y components. Then add the components.
 
How do I know what the other angles are aside from 90 degrees?
 
You can use the tangent to find them, since you know the length of the adjacent and opposite sides.
 
eddiedowen said:
How do I know what the other angles are aside from 90 degrees?
The problem statement gives one of the angles of each triangle. Did you remember that the complementary angles of a right triangle sum to 90 degrees?
 
Eddie, you need to complete the template before we can help you.
 

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