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Problem a) Why can line L be bisected? I know to make a triangle by making θ on the horizon, but I don't know why this bisects L. Is there a mathematical or geometric basis?

Problem a) Why can line L be bisected? I know to make a triangle by making θ on the horizon, but I don't know why this bisects L. Is there a mathematical or geometric basis?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem a)

Why can line L be bisected?
I know to make a triangle by making θ on the horizon, but I don't know why this bisects L. Is there a mathematical or geometric basis?

目 Chapter 4.2, Problem 4.87P A slender rod BC with a length of L and weight W is held by two cables as shown. Knowing that cable AB is horizontal and that the rod forms an angle of 40° with the horizontal, determine (a) the angle that cable CD forms with the horizontal, (b) the tension in each cable. Chapter 4.2, Problem 4.87P, A slender rod BC with a length of L and weight W is held by two cables as shown. Knowing that cable Fig. P4.87 VECTOR MECHANICS FOR ENGINEERS STATICS 40° A B 그림 P4.77 C D BUY THIS BOOK Vector Mechanics for Engineers: Statics 12th Edition Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek Publisher: McGraw-Hill Education ISBN: 9781259977268
Transcribed Image Text:目 Chapter 4.2, Problem 4.87P A slender rod BC with a length of L and weight W is held by two cables as shown. Knowing that cable AB is horizontal and that the rod forms an angle of 40° with the horizontal, determine (a) the angle that cable CD forms with the horizontal, (b) the tension in each cable. Chapter 4.2, Problem 4.87P, A slender rod BC with a length of L and weight W is held by two cables as shown. Knowing that cable Fig. P4.87 VECTOR MECHANICS FOR ENGINEERS STATICS 40° A B 그림 P4.77 C D BUY THIS BOOK Vector Mechanics for Engineers: Statics 12th Edition Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek Publisher: McGraw-Hill Education ISBN: 9781259977268
Explanation of Solution The free-body diagram corresponding to the arrangement in Fig. P4.87 is given in Figure 1. The tension in the cable CD and cable AB are represented by TCD and TAB respectively. The weight of the rod acting vertically downward is represented by W. The line of action of TCD must pass through the point Ę, where TAB and W intersect. 12 L TCD TAB B L 40° Ꮎ E F L sin 40° L sin 40° Figure 1 Write the expression for the distance CF from the free-body diagram. CF = L sin 40° (1) Here, is the length of the rod. Write the expression for the distance EF from the free-body diagram. EF = L cos 40° (II) Write the expression for computing the angle 0 from the free-body diagram. CF (111) tan 0 = EF
Transcribed Image Text:Explanation of Solution The free-body diagram corresponding to the arrangement in Fig. P4.87 is given in Figure 1. The tension in the cable CD and cable AB are represented by TCD and TAB respectively. The weight of the rod acting vertically downward is represented by W. The line of action of TCD must pass through the point Ę, where TAB and W intersect. 12 L TCD TAB B L 40° Ꮎ E F L sin 40° L sin 40° Figure 1 Write the expression for the distance CF from the free-body diagram. CF = L sin 40° (1) Here, is the length of the rod. Write the expression for the distance EF from the free-body diagram. EF = L cos 40° (II) Write the expression for computing the angle 0 from the free-body diagram. CF (111) tan 0 = EF
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