Math Problem Statement

Two vectors are given below. Determine the magnitude in N of the resultant sum of the two vectors.

A = 80.3 N, 74.0 degrees above the positive x-axis

B = 83.1 N, 67.5 degrees above the negative x-axis

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Addition
Trigonometry
Pythagorean Theorem

Formulas

Ax = A * cos(θA)
Ay = A * sin(θA)
Bx = B * cos(θB)
By = B * sin(θB)
Resultant Magnitude: |R| = √(Rx² + Ry²)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 10-12