10. A guy wire attached to a vertical pole of height 18 m
is 24 m long and has a stake attached to the other
end. How far from the base of the pole should the
stake be driven so that the wire will be taut?
Answers
Given :
☞ Height = 18 m.
☞ Length = 24 m.
According to the question :
Right Triangle ABC,
Pythagoras theorem,
=> AC^2 = AB^2 + BC^2
=> 24^2 = 18^2 + BC^2
=> 576 = 324 + BC^2
=> BC^2 = 576 - 324
=> BC^2 = 252
=> BC = √252
=> BC = √ 2 × 2 × 3 × 3 × 7
=> BC = 2 × 3 × 7
=> BC = 6 √ 7 m.
BC = 6 √ 7 m.
Question:-
A guy wire attached to a vertical pole of height 18m is 24m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
Solution:-
Given:- a) a guy wire attached to a vertical pole of height 18m is 24m long. {height of pole is 18m & length of wire is 24m .}
b) a stake attached to the other end.
Find :- How far from the base of the pole should the stake be driven so that the wire will be taut ? { the distance from base of pole to stake }
so now
Let, AB be the pole and AC be the wire & BC be the distance from base of pole to stake { stake at point C } .
we know that pole is perpendicular to it's base mean's pole AB create an angle of 90° with base BC. { pole is situated on ground so we assume that pole perpendicular to it's base ( ground ) } .
Hence we assume that ABC is a right angle triangle. so, we know
• Pole ( AB ) = 18m,
• Wire { AC (hypotenuse) } = 24 m
• Distance between base of pole to stake BC = ?
Hence, to find the distance from base of pole to stake which is BC
so we use,
Pythagoras theorem
=> ( AC )² = ( AB )² + ( BC )²
=> ( 24 )² = ( 18 )² + ( BC )²
=> 576 = 324 + ( BC )² i.e.
=> ( BC )² + 324 = 576
=> ( BC )² = 576 - 324
=> ( BC )² = 252
=> BC = √252
=> BC = √2 × 2 × 3 × 3 × 7
=> BC = 2×3√7
=> BC = 6√7 m
Hence wire 6√7 m far from the base of the pole should the stake be driven so that the wire will be taut.
i hope it helps you.
