Answered: espectively with the positive x-axis.…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section: Chapter Questions

Problem 16T

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Question

Three forces with magnitudes 80lbs, 120lbs, and 60lbs, act on an object at angles 45°, 60°, and 30° respectively with the positive x-axis. Find the magnitude and direction angle from the positive x-axis of the resultant force (round to two decimal places.)

Expert Solution

Step 1

magnitude:

$F_{1} = 80 \cos (45 °) i + 80 \sin (45 °) j = 80 \frac{1}{\sqrt{2}} i + 80 \frac{1}{\sqrt{2}} j = 40 \sqrt{2} i + 40 \sqrt{2} j F_{2} = 120 \cos (60 °) i + 120 \sin (60 °) j = 60 i + 60 \sqrt{3} j F_{3} = 60 \cos (30 °) i + 60 \sin (30 °) j = 30 \sqrt{3} i + 30 j F_{1} + F_{2} + F_{3} = (40 \sqrt{2} + 60 + 30 \sqrt{3}) i + (40 \sqrt{2} + 60 \sqrt{3} + 30) j$

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