# Finding the resultant of two vectors

• eddiedowen
In summary, the problem involves finding the resultant of two vectors, S and T, which have magnitudes and angles specified. To solve this, the vectors are broken down into rectangular components using cosine and sine, and then added together. The complementary angles of the right triangles formed can be used to find the missing angles.
eddiedowen

## 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.

## The Attempt at a Solution

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.

## What is the definition of a vector?

A vector is a mathematical object that has both magnitude and direction. It is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

## How do you find the resultant of two vectors?

The resultant of two vectors is found by adding the two vectors together. This can be done by using vector addition, which involves breaking down the vectors into their components and adding the corresponding components together.

## What is the difference between scalar and vector quantities?

Scalar quantities only have magnitude and no direction, such as speed or temperature. Vector quantities have both magnitude and direction, such as velocity or force.

## Why is it important to find the resultant of two vectors?

Finding the resultant of two vectors is important because it allows us to determine the overall magnitude and direction of the combined effects of the two individual vectors. This is useful in many fields, such as physics, engineering, and navigation.

## What are some practical applications of finding the resultant of two vectors?

Finding the resultant of two vectors is used in many practical applications, such as calculating the trajectory of a projectile, determining the net force on an object, and calculating the total displacement of an object. It is also used in fields such as transportation, architecture, and sports.

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