The length of the wire is 37.15 ft
Explanation:
The figure is attached for the reference.
tan (71) = [tex]\frac{y}{x}[/tex]
tan (36) = [tex]\frac{y}{36+x}[/tex]
So,
tan(36) (36 + x) = y
tan(71) = [tex]\frac{tan (36) (36 + x )}{x}[/tex]
[tex]2.9 = \frac{0.73 (36 + x)}{x} \\\\2.9 x = 26.28 + 0.73x\\\\2.17x = 26.28\\\\x = 12.11 ft[/tex]
Substituting x = 12.11 ft in equation 1:
[tex]tan (71) = \frac{y}{12.11} \\\\2.9 X 12.11 = y\\\\y = 35.119 ft[/tex]
Length of the wire, z = [tex]\sqrt{x^2 + y^2}[/tex]
So,
[tex]z = \sqrt{(12.11)^2 + (35.119)^2} \\\\z = \sqrt{146.6521 + 1233.3442} \\\\z = 37.15 ft[/tex]
Therefore, the length of the wire is 37.15 ft
