a wire of 18 m length had been tied with electric pole at an angle of elevation 30 degrees with the ground.because it was covering a long distance it was cut and tied at an angle of elevation of 60 degrees with the ground. how much length of the wire was cut.
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first, sinA=P/H
here, sin30=1/2
H=18 m
so,P/H=1/2
or,P=H/2=9 m
In second case, the length of the pole i.e. P=9 m will be the same.
sin60=√3/2=P/H
here we have to find H.
so,H=(9x2)/√3
=18/√3
=(18x√3)/3
=6x√3=6x1.72(approx.)=10.32
so, new length=10.32
so,decrease in length=18-10.32 m=7.68 m.
Here,P is the perpendicular & H is the hypotenuse of a right angled triangle which
is formed by the above arrangements. The right angle is formed at the point where the pole meets the ground.This method has strictly been done in accordance with the formulas of trigonometric standard angles' values.
here, sin30=1/2
H=18 m
so,P/H=1/2
or,P=H/2=9 m
In second case, the length of the pole i.e. P=9 m will be the same.
sin60=√3/2=P/H
here we have to find H.
so,H=(9x2)/√3
=18/√3
=(18x√3)/3
=6x√3=6x1.72(approx.)=10.32
so, new length=10.32
so,decrease in length=18-10.32 m=7.68 m.
Here,P is the perpendicular & H is the hypotenuse of a right angled triangle which
is formed by the above arrangements. The right angle is formed at the point where the pole meets the ground.This method has strictly been done in accordance with the formulas of trigonometric standard angles' values.
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