A post is supported by two wires (one on each side going in opposite directions) creating an angle of 80° between the wires. The ends of the wires are 12m apart on the ground with one wire forming an angle of 40° with the ground. To the nearest meter, how much wire was used to support the post?
WITH WORK PLEASE
Answers
Given : A post is supported by two wires (one on each side going in opposite directions) creating an angle of 80° between the wires. The ends of the wires are 12m apart on the ground with one wire forming an angle of 40° with the ground.
To find : how much wire was used to support the post
Solution:
Angle between wires = 80°
Angle by one wire with ground = 40°
Angle by another Wire with ground = 180° - (80° + 40° ) = 60°
Using Sine formula of triangle
one side wire length / Sin 40° =Another side wire length/ Sin 60° = 12/Sin80°
=> one side wire length = 12 Sin40° /Sin 80° = 7.83 m
Another Side wire length = 12 Sin60° /Sin 80° = 10.55 m
Total length of Wire used = 7.83 + 10.55
= 18.38 m
Let say pillar height = h
& Distance of pillar bottom from wire at ground on side making angle 40° = x m , then from another wire = 12 - x m
=> Tan 40° = h/x
=> h = x Tan 40°
from another wire
& Tan 60° = h/(12- x)
=> h = (12 -x)Tan60°
x Tan 40° = (12 - x) Tan60
=> x = 8.08 m
& h = 6.78 m
Wire length = √x² + h² + √(12-x)² + h²
= 10.548 + 7.832
= 18.38 m
≈ 18 m
Length of wire used to support the post = 18.38 m ≈ 18 m
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