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A ladder 12m long just reaches the top of a vertical wall. If the ladder makes an angle of 45° with the wall, then the height of the wall is
- a)12m
- b)6m
- c)12√2m
- d)6√2m
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A ladder 12m long just reaches the top of a vertical wall. If the ladd...
° with the ground, what is the distance between the wall and the base of the ladder?
Let's call the distance between the wall and the base of the ladder "x".
We can use trigonometry to solve for x.
We know that the ladder is 12m long and makes an angle of 45° with the ground. This means that the opposite side (the distance between the wall and the ladder) and the adjacent side (the distance between the base of the ladder and the wall) are equal.
Using the trigonometric function for tangent (tan), we can set up the following equation:
tan(45°) = opposite/adjacent
tan(45°) = x/12
We can solve for x by multiplying both sides by 12:
x = 12 * tan(45°)
Using a calculator, we can find that tan(45°) is equal to 1.
So, x = 12 * 1 = 12m.
Therefore, the distance between the wall and the base of the ladder is 12m.
Let's call the distance between the wall and the base of the ladder "x".
We can use trigonometry to solve for x.
We know that the ladder is 12m long and makes an angle of 45° with the ground. This means that the opposite side (the distance between the wall and the ladder) and the adjacent side (the distance between the base of the ladder and the wall) are equal.
Using the trigonometric function for tangent (tan), we can set up the following equation:
tan(45°) = opposite/adjacent
tan(45°) = x/12
We can solve for x by multiplying both sides by 12:
x = 12 * tan(45°)
Using a calculator, we can find that tan(45°) is equal to 1.
So, x = 12 * 1 = 12m.
Therefore, the distance between the wall and the base of the ladder is 12m.
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Community Answer
A ladder 12m long just reaches the top of a vertical wall. If the ladd...
Let the length of the ladder be =12m(hypotenuse)
The angle between the ladder and the wall ∠BCA=45degree
Angle between ladder and the ground ∠CAB=90 −45 = 45 degree
Height of the wall =BC
Sin 45 degree = BC/12
1/√2 = BC/12
√2BC = 12
BC = 12/√2 = √144/√2 = (√2×2×2×2×3×3)/√2
we are left with (√2×2×2×3×3) = 6√2 m
The angle between the ladder and the wall ∠BCA=45degree
Angle between ladder and the ground ∠CAB=90 −45 = 45 degree
Height of the wall =BC
Sin 45 degree = BC/12
1/√2 = BC/12
√2BC = 12
BC = 12/√2 = √144/√2 = (√2×2×2×2×3×3)/√2
we are left with (√2×2×2×3×3) = 6√2 m
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A ladder 12m long just reaches the top of a vertical wall. If the ladder makes an angle of 45° with the wall, then the height of the wall isa)12mb)6mc)12√2md)6√2mCorrect answer is option 'D'. Can you explain this answer?
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