Length of one side of rope is 31.5958 feet and length of other side is 26.828 feet
Step-by-step explanation:
We are given distance between ropes = 40 feet
Angle between two ropes = 86 degrees
Angle of elevation of one rope = 42 degrees
We need to find the length of both ropes
First finding angle of elevation of 2nd rope:
180 - (86+42)=Angle of elevation of 2nd rope
Angle of elevation of 2nd rope = 52 degrees
Now finding sides of rope (see reference of figure attached)
Using Law of Sines:
[tex]\frac{Sin(C)}{c}=\frac{Sin(B)}{b}[/tex]
Putting values of angle C and B and side c to find side
[tex]\frac{sin(86)}{40}=\frac{sin(52)}{b} \\b(sin(86)=40(sin(52))[/tex]
[tex]b(0.9976)=40(0.7880)\\b(0.9976)=31.52\\b=\frac{31.52}{0.9976}\\b=31.5958\,\,feet[/tex]
So, Length of side b is 31.5958 feet
Similarly finding length of side a
Using Law of Sines:
[tex]\frac{Sin(A)}{a}=\frac{Sin(C)}{c}[/tex]
Putting values of angle C and B and side c to find side
[tex]\frac{sin(42)}{a}=\frac{sin(86)}{40} \\40(sin(42)=a(sin(86))[/tex]
[tex]40(0.6691)=a(0.9976)\\26.764=a(0.9976)\\a=\frac{26.764}{0.9976}\\a=26.828\,\,feet[/tex]
So, length of side a is 26.828 feet
Therefore, length of one side of rope is 31.5958 feet and length of other side is 26.828 feet
