SOLUTION: a ladder 9m long is placed against a wall 2m away from its base. what is the height reached by the ladder? find the approximate distance that will be saved by walking diagonally

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Question 535976: a ladder 9m long is placed against a wall 2m away from its base. what is the height reached by the ladder?
find the approximate distance that will be saved by walking diagonally across a field 450m by 250m instead of walking along the two adjacent sides.
A flagpole is to be made firm. how much wire will be needed if, from 3 pegs, each 120cm away from the foot of the people, wire will be tied to a point on the pole 2and1/2m from the ground?

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The ladder,the floor & the wall form a right triangle.
The base is one leg The height is the other leg
The ladder acts as the hypotenuse
Pythagoras theorem

(Hyp)^2= (leg1)^2+ Leg2^2
Hypotenuse = 9 ft
leg1= 2 ft
Leg2= ?

leg2^2=hyp^2-leg1^2
Leg2^2= 9^2-2^2
Leg2^2= 81-4
Leg2^2=77
Leg2= sqrt%28175%29
Leg2= 8.77 ft --- The height it reaches

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The sides and the diagonal form a right triangle
The length is one leg & the width is the other leg
One leg 450 m
Second leg 250 m
Hypotenuse x m
By Pythagoras theorem
Hypotenuse^2 = Leg1^2+leg2^2
+%09x+%09%5E2%09=%09450%09%5E2%09%2B%09250%09%5E2
x ^2 = 202500 + 62500
x ^2 = 265000
+sqrt%28x%5E2%29=%09%09sqrt%28%09265000%09%29
x= 514.78 m

The sum of the sides = 700 m
The diagonal = 514.78 m

The difference= 185.22 m

185.22 m will be saved
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The rope forms the hypotenuse of the right triangle
One leg 250 cm
Second leg 120 cm
Hypotenuse x cm
By Pythagoras theorem
Hypotenuse^2 = Leg1^2+leg2^2
+%09x+%09%5E2%09=%09250%09%5E2%09%2B%09120%09%5E2
x ^2 = 62500 + 14400
x ^2 = 76900
+sqrt%28x%5E2%29=%09%09sqrt%28%0976900%09%29
x= 277.31 cm the length of the rope.
There are 3 ropes . multiply by 3 to get the total length required


m.ananth@hotmail.ca