Solving Vector Components and Theta with Pythagorean Theorem

In summary, the conversation discusses finding the magnitude and angle of a resultant vector given three vector components. The suggested methods for finding the angle include using the Pythagorean Theorem and basic trigonometry, specifically using the tangent function. The conversation also mentions setting up the x and y components of the vector to calculate the angle.
  • #1
ColinTI89
2
0

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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  • #2
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]
 

What is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical principle that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

How is the Pythagorean Theorem used to solve vector components?

In physics and engineering, vectors are often represented using their components in the x and y directions. The Pythagorean Theorem can be used to find the magnitude of the vector by taking the square root of the sum of the squares of the x and y components.

What is the difference between magnitude and direction in vector components?

Magnitude refers to the size or length of a vector, while direction refers to the angle or orientation of the vector. In solving for vector components using the Pythagorean Theorem, the magnitude is calculated first, followed by the direction.

Can the Pythagorean Theorem be used to solve for vector components in three dimensions?

Yes, the Pythagorean Theorem can be extended to three dimensions, where it is known as the Pythagorean Theorem in 3D. In this case, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides in all three dimensions.

How is the Pythagorean Theorem used in real-world applications?

The Pythagorean Theorem is used in various fields such as engineering, physics, and navigation. It is used to solve for unknown sides or angles in right triangles, which can then be applied to real-world problems involving forces, velocities, and distances.

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