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# The base of a 20-foot rope is 8 feet above the ground. If the rope is

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Math Expert
Joined: 02 Sep 2009
Posts: 53005
The base of a 20-foot rope is 8 feet above the ground. If the rope is  [#permalink]

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17 Jan 2019, 23:14
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:35) correct 38% (01:18) wrong based on 29 sessions

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The base of a 20-foot rope is 8 feet above the ground. If the rope is extended at a 60-degree angle, the top of the rope will be how many feet above the ground?

A 18
B 28
C 10√3
D 10√2 + 8
E 10√3 + 8

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Joined: 18 Aug 2017
Posts: 1842
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The base of a 20-foot rope is 8 feet above the ground. If the rope is  [#permalink]

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18 Jan 2019, 05:42
Bunuel wrote:
The base of a 20-foot rope is 8 feet above the ground. If the rope is extended at a 60-degree angle, the top of the rope will be how many feet above the ground?

A 18
B 28
C 10√3
D 10√2 + 8
E 10√3 + 8

draw figure
base is 8 feet above ground , angle 60* subtended at base so rope is making 30:60:90 triangle
30 ; 10
so and 60 * = 10 sqrt 3
height of top of rope 10√3 + 8
IMO E
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Intern
Joined: 12 Sep 2018
Posts: 21
Re: The base of a 20-foot rope is 8 feet above the ground. If the rope is  [#permalink]

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19 Jan 2019, 02:54
Archit3110 wrote:
Bunuel wrote:
The base of a 20-foot rope is 8 feet above the ground. If the rope is extended at a 60-degree angle, the top of the rope will be how many feet above the ground?

A 18
B 28
C 10√3
D 10√2 + 8
E 10√3 + 8

draw figure
base is 8 feet above ground , angle 60* subtended at base so rope is making 30:60:90 triangle
30 ; 10
so and 60 * = 10 sqrt 3
height of top of rope 10√3 + 8
IMO E

How do we know that the 6o° angle is formed between the rope and the ground and not the angle at the top of the rope?
SVP
Joined: 18 Aug 2017
Posts: 1842
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The base of a 20-foot rope is 8 feet above the ground. If the rope is  [#permalink]

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19 Jan 2019, 03:21
artiom01 wrote:
Archit3110 wrote:
Bunuel wrote:
The base of a 20-foot rope is 8 feet above the ground. If the rope is extended at a 60-degree angle, the top of the rope will be how many feet above the ground?

A 18
B 28
C 10√3
D 10√2 + 8
E 10√3 + 8

draw figure
base is 8 feet above ground , angle 60* subtended at base so rope is making 30:60:90 triangle
30 ; 10
so and 60 * = 10 sqrt 3
height of top of rope 10√3 + 8
IMO E

How do we know that the 6o° angle is formed between the rope and the ground and not the angle at the top of the rope?

artiom01

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Re: The base of a 20-foot rope is 8 feet above the ground. If the rope is   [#permalink] 19 Jan 2019, 03:21
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