Three math instructors are trying to hold a sedated bear in the center of a class-room. There are three ropes attached to the bear and each instructor has hold of arope. Mark is pulling in the direction 15° East of North with a force of 20 poundsand Allison is pulling in the direction 25° East of South with a force of 30 pounds.You must quickly tell Joe the compass direction and the magnitude of the forcewhich must be exerted on the third rope to counterbalance Mark and Allison.(Give approximate answers to three decimal places.)

Answered: Three math instructors are trying to…

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter2: Right Triangle Trigonometry

Section: Chapter Questions

Problem 29CT

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Three math instructors are trying to hold a sedated bear in the center of a class-
room. There are three ropes attached to the bear and each instructor has hold of a
rope. Mark is pulling in the direction 15° East of North with a force of 20 pounds
and Allison is pulling in the direction 25° East of South with a force of 30 pounds.
You must quickly tell Joe the compass direction and the magnitude of the force
which must be exerted on the third rope to counterbalance Mark and Allison.
(Give approximate answers to three decimal places.)

Expert Solution

Step 1

Let, Joe is pulling the rope wit force $F_{3} pounds$ in the direction of $θ$ degrees north of west.

Forces of equilibrium along $x - direction$ .

$\begin{array}{rcl} F_{1} \sin 15 ° + F_{2} \sin 25 ° - F_{3} \cos θ & = & 0 \\ F_{3} \cos θ & = & 20 \cdot \sin 15 ° + 30 \cdot \sin 25 ° \\ = & 5.176 + 12.678 \\ = & 17.854 . . . . (1) \end{array}$

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