A 25 ft ladder is placed with its foot 7 ft away from a building. If the top of the ladder slips down 4 ft, how many feet will the bottom slide out?
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8 ft
First triangle: 7 squared + 24 squared = 25 squared, so the top of the ladder was 24 feet high.
24 - 4= 20. 25 squared - 20 squared = 225. Take the square root of that and you get 15: the new base of the triangle. 15 - 7 (the old base) = 8ft
First triangle: 7 squared + 24 squared = 25 squared, so the top of the ladder was 24 feet high.
24 - 4= 20. 25 squared - 20 squared = 225. Take the square root of that and you get 15: the new base of the triangle. 15 - 7 (the old base) = 8ft
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This is not as hard as it looks. The ladder is forming a right triangle, with a bottom base of 7 and a hypotenuse of 25. Solve for the side:
a^2 + 7^2 = 25^2
a^2 + 49 = 625
a^2 = 576
a = 24
So the ladder is resting at a point 24 feet from the bottom. If the ladder suddenly slips down 4 feet, it will be resting at a point 20 feet from the bottom. The length of the ladder has not changed; therefore, the foot of the ladder will have slid out a number of feet. It is still a right triangle, so you still just need to solve for the bottom instead of the side:
20^2 + b^2 = 25^2
400 + b^2 = 625
b^2 = 225
b = 15
So the bottom will now be 15 feet out from the building instead of 7 feet, so it will have slid out 8 feet.
a^2 + 7^2 = 25^2
a^2 + 49 = 625
a^2 = 576
a = 24
So the ladder is resting at a point 24 feet from the bottom. If the ladder suddenly slips down 4 feet, it will be resting at a point 20 feet from the bottom. The length of the ladder has not changed; therefore, the foot of the ladder will have slid out a number of feet. It is still a right triangle, so you still just need to solve for the bottom instead of the side:
20^2 + b^2 = 25^2
400 + b^2 = 625
b^2 = 225
b = 15
So the bottom will now be 15 feet out from the building instead of 7 feet, so it will have slid out 8 feet.
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8 ft. one side of a triangle is 7 ft (the ground) and the ladder (hypotenuse) is 25 ft, use the pythagorean theorem to find the length of the third side or the wall which is 24 ft. if it slides down the wall 4 ft, it loses 4, making that side 20 ft. the ladder is still 25 ft, so use the pythagorean theorem again to find the remaining side.
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The ladder is laid down to a wall. So it forms a right-angled triangle.
Then we can get the height of the ladder laid is: 25^2-7^2=24^2
If the ladder slips down 4 ft, the height should be 20 ft left. And the ladder is 25ft.
We can get: 25^2-20^2=15^2
15ft-7ft=8ft
So 8ft will the bottom slide out.
Then we can get the height of the ladder laid is: 25^2-7^2=24^2
If the ladder slips down 4 ft, the height should be 20 ft left. And the ladder is 25ft.
We can get: 25^2-20^2=15^2
15ft-7ft=8ft
So 8ft will the bottom slide out.
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Firstly - how far up wall does ladder reach - ?
Diagram would show formation of right-angled triangle with ladder as hypotenuse
Use Pythagoras - to get answer - 24ft
So if ladder slips down 4 ft, its height is now 20ft
Use Pythagoras again to get - ladder is now 15ft from wall.
Slippage is therefore 15ft - 7 ft
=????? !
Diagram would show formation of right-angled triangle with ladder as hypotenuse
Use Pythagoras - to get answer - 24ft
So if ladder slips down 4 ft, its height is now 20ft
Use Pythagoras again to get - ladder is now 15ft from wall.
Slippage is therefore 15ft - 7 ft
=????? !
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