Solving Vector Components and Theta with Pythagorean Theorem

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SUMMARY

The discussion focuses on solving for the angle theta of a resultant vector using the Pythagorean theorem and basic trigonometry. The vectors involved are Vector A (5.00 m), Vector B (17.0 m), and Vector C (15.0 m). The key to finding theta is to first determine the X and Y components of the resultant vector, which can be expressed in the form of x̂i + ŷj. The angle with the horizontal can then be calculated using the formula tan(theta) = y/x.

PREREQUISITES
  • Pythagorean Theorem
  • Basic Trigonometry
  • Vector Component Analysis
  • Understanding of Angles in Geometry
NEXT STEPS
  • Learn how to decompose vectors into their X and Y components
  • Study the application of the Pythagorean theorem in vector addition
  • Explore trigonometric functions for angle calculations
  • Practice problems involving resultant vectors and angles
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on vector analysis and trigonometry. This discussion is beneficial for anyone needing to solve problems involving vector components and angles.

ColinTI89
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Homework Statement


Vector A= 5.00 m (See the attached image for the graphical representation)
Vector B=17.0m
Vector C=15.0 m


Homework Equations



Pythagorean Theorem, Basic trigonometry

The Attempt at a Solution



Finding the magnitude of the resultant vector is not where I'm having issues. I just can't figure out how to find theta (the angle of depression of the resultant vector). The only thing I could think of is to set up the X and Y components of the vector, but I don't know the lengths of those so I can't get any futher than that to calculate the angle.

Thanks in Advance,
Colin
 

Attachments

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i'm bad with geometry so i can only tell you that find each vector in form of: [tex]x\hat{i} + y\hat{j}[/tex]

find net of all vectors

then angle with horizontal is: [tex]tan\theta = \frac{y}{x}[/tex]
 

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