Calculate Vector Addition with Trigonometry and Pythagorean Theorem

How do we calculate vector addition using trigonometry and the Pythagorean theorem?

Given vector A with a magnitude of 122 cm at 145° and vector B with 110 cm at 270°, how can we find the resultant vector?

Calculating Vector Addition with Trigonometry and Pythagorean Theorem

To calculate vector addition using trigonometry and the Pythagorean theorem, we first need to break down each vector into its horizontal and vertical components. Then, we add the components separately and finally use trigonometry to find the magnitude and direction of the resultant vector.

Vector addition involves combining two vectors to determine their combined effect. In this scenario, vector A has a magnitude of 122 cm at an angle of 145°, while vector B has a magnitude of 110 cm at an angle of 270°.

By breaking down each vector into its horizontal and vertical components, we can add these components separately to find the resultant vector. After finding the magnitude and direction of the resultant vector using trigonometry and the Pythagorean theorem, we will have the final answer that represents the combined effect of vectors A and B.

Understanding vector addition is crucial in various fields such as physics, engineering, and mathematics. It allows us to determine the total effect of multiple vectors acting on a point and is essential for solving problems involving forces, velocities, and displacements.

By mastering the principles of vector addition, including trigonometry and the Pythagorean theorem, we can accurately calculate the resultant vector and analyze complex vector systems effectively.