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# A 10-foot ladder leans against a vertical wall and forms a 60-degree a

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
A 10-foot ladder leans against a vertical wall and forms a 60-degree a  [#permalink]

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09 Oct 2018, 01:09
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Difficulty:

25% (medium)

Question Stats:

82% (00:53) correct 18% (00:37) wrong based on 23 sessions

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A 10-foot ladder leans against a vertical wall and forms a 60-degree angle with the floor. If the ground below the ladder is horizontal, how far above the ground is the top of the ladder?

(A) $$5$$ feet

(B) $$5\sqrt{3}$$ feet

(C) $$7.5$$ feet

(D) $$10$$ feet

(E) $$10\sqrt{3}$$ feet

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Re: A 10-foot ladder leans against a vertical wall and forms a 60-degree a  [#permalink]

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09 Oct 2018, 08:36
Bunuel wrote:
A 10-foot ladder leans against a vertical wall and forms a 60-degree angle with the floor. If the ground below the ladder is horizontal, how far above the ground is the top of the ladder?

(A) $$5$$ feet

(B) $$5\sqrt{3}$$ feet

(C) $$7.5$$ feet

(D) $$10$$ feet

(E) $$10\sqrt{3}$$ feet

$$Cos 60 = \frac{Base}{Hypot} = \frac{1}{2}$$

Or, $$\frac{B}{10} = \frac{1}{2}$$

So, $$B = 5$$ , Answer must be (A)
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Re: A 10-foot ladder leans against a vertical wall and forms a 60-degree a  [#permalink]

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09 Oct 2018, 10:52
Bunuel wrote:
A 10-foot ladder leans against a vertical wall and forms a 60-degree angle with the floor. If the ground below the ladder is horizontal, how far above the ground is the top of the ladder?

(A) $$5$$ feet

(B) $$5\sqrt{3}$$ feet

(C) $$7.5$$ feet

(D) $$10$$ feet

(E) $$10\sqrt{3}$$ feet

if the angle with the floor is 60 degrees.

then it is 30:60:90

x:$$x\sqrt{3}$$:2x

the hypotenuse is 10 so 10 =2x

x = 5

the horizontal distance would then be 5
and the vertical distance (that is the distance opposing the 60-angle degree) = $$5\sqrt{3}$$

Re: A 10-foot ladder leans against a vertical wall and forms a 60-degree a   [#permalink] 09 Oct 2018, 10:52
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