It is currently 20 Oct 2017, 07:39

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A ladder of a fire truck is elevated to an angle of 60° and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Intern
Intern
avatar
Joined: 12 May 2012
Posts: 25

Kudos [?]: 197 [3], given: 19

Location: United States
Concentration: Technology, Human Resources
A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 07 Jun 2012, 01:16
3
This post received
KUDOS
23
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (01:24) correct 23% (01:37) wrong based on 1408 sessions

HideShow timer Statistics

A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

(A) 35
(B) 42
(C) \(35\sqrt{3}\)
(D) \(7 + 35\sqrt{3}\)
(E) \(7 + 42\sqrt{3}\)
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Dec 2012, 05:04, edited 1 time in total.
Edited the question.

Kudos [?]: 197 [3], given: 19

1 KUDOS received
Intern
Intern
avatar
Status: ISB 14...:)
Joined: 26 May 2012
Posts: 30

Kudos [?]: 40 [1], given: 11

Location: India
Concentration: Strategy
Schools: ISB '14 (A)
GMAT 1: 750 Q51 V39
GPA: 3.62
WE: Engineering (Energy and Utilities)
Reviews Badge
Re: maths problem [#permalink]

Show Tags

New post 07 Jun 2012, 01:47
1
This post received
KUDOS
Vertical height of ladder = 70.sin(60) = 35root3

Total height = 7 + 35root3

Kudos [?]: 40 [1], given: 11

Expert Post
6 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128977 [6], given: 12185

Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 07 Jun 2012, 11:50
6
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
Notice that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

sarb wrote:
A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many meet above the ground does the ladder reach?

A. 35
B. 42
C. 35 root 3
D. 7 + 35 root 3
E. 7 + 42 root 3


Look at the diagram below:
Attachment:
Ladder.png
Ladder.png [ 5.44 KiB | Viewed 30206 times ]
Triangle ABC is a 30°-60°-90° triangle. Now, in a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\), the leg opposite 30° (AC) corresponds with \(1\), the leg opposite 60° (BC) corresponds with \(\sqrt{3}\) and the hypotenuse AC corresponds with 2. So, \(\frac{BC}{AB}=\frac{\sqrt{3}}{2}\) --> \(\frac{BC}{70}=\frac{\sqrt{3}}{2}\) --> \(BC=35\sqrt{3}\).

Hence the leader reaches \(7+35\sqrt{3}\) above the ground.

Answer: D.

For more check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128977 [6], given: 12185

Intern
Intern
avatar
Joined: 12 May 2012
Posts: 25

Kudos [?]: 197 [0], given: 19

Location: United States
Concentration: Technology, Human Resources
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 07 Jun 2012, 19:21
Bunuel wrote:
Notice that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

sarb wrote:
A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many meet above the ground does the ladder reach?

A. 35
B. 42
C. 35 root 3
D. 7 + 35 root 3
E. 7 + 42 root 3


Look at the diagram below:
Attachment:
Ladder.png
Triangle ABC is a 30°-60°-90° triangle. Now, in a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\), the leg opposite 30° (AC) corresponds with \(1\), the leg opposite 60° (BC) corresponds with \(\sqrt{3}\) and the hypotenuse AC corresponds with 2. So, \(\frac{BC}{AB}=\frac{\sqrt{3}}{2}\) --> \(\frac{BC}{70}=\frac{\sqrt{3}}{2}\) --> \(BC=35\sqrt{3}\).

Hence the leader reaches \(7+35\sqrt{3}\) above the ground.

Answer: D.

For more check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.


Thank you that made it very simple :)

Kudos [?]: 197 [0], given: 19

VP
VP
avatar
S
Joined: 09 Jun 2010
Posts: 1403

Kudos [?]: 159 [0], given: 916

Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 21 Feb 2013, 10:31
which one of 2 angles is 60?

the question is not clear.
_________________

visit my facebook to help me.
on facebook, my name is: thang thang thang

Kudos [?]: 159 [0], given: 916

Manager
Manager
User avatar
Joined: 24 Sep 2012
Posts: 90

Kudos [?]: 168 [0], given: 3

Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 21 Feb 2013, 10:38
Since the questions says elevated at an angle of 60 deg, the base angle is 60 deg. By default, elevation is from baseline and since the ladder is placed parallel to x axis, the elevation is also from x axis.

Hope that helps!

thangvietnam wrote:
which one of 2 angles is 60?

the question is not clear.

Kudos [?]: 168 [0], given: 3

Intern
Intern
User avatar
Joined: 18 May 2013
Posts: 7

Kudos [?]: 9 [0], given: 55

Location: Germany
GMAT Date: 09-27-2013
GMAT ToolKit User
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 22 Jul 2013, 10:44
I do not get the ratio 1 : 2 : √3 :?:

For me it is 1 : 2 : 3 (30° : 60° : 90°)... can anyone help?

Thanks in advance!

Kudos [?]: 9 [0], given: 55

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128977 [2], given: 12185

Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 22 Jul 2013, 10:48
2
This post received
KUDOS
Expert's post

Kudos [?]: 128977 [2], given: 12185

Intern
Intern
User avatar
Joined: 18 May 2013
Posts: 7

Kudos [?]: 9 [0], given: 55

Location: Germany
GMAT Date: 09-27-2013
GMAT ToolKit User
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 22 Jul 2013, 10:51
Bunuel wrote:
sv3n wrote:
I do not get the ratio 1 : 2 : √3 :?:

For me it is 1 : 2 : 3 (30° : 60° : 90°)... can anyone help?

Thanks in advance!


Check Triangles chapter of Math Book: ...

Hope it helps.


OK.. IT´S GIVEN. :-D

Thanks a lot! :!:

Kudos [?]: 9 [0], given: 55

Intern
Intern
avatar
Joined: 03 Aug 2013
Posts: 1

Kudos [?]: [0], given: 0

Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 29 Dec 2013, 11:00
I understand the ratio x:x(sqrt)3:2x and how to get 7+35sqrt3, but how is this not a 3-4-5 right triangle with lengths of 42-56-70? Thank you for the added explanation.

Kudos [?]: [0], given: 0

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128977 [0], given: 12185

Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 29 Dec 2013, 11:16
bgourlay13 wrote:
I understand the ratio x:x(sqrt)3:2x and how to get 7+35sqrt3, but how is this not a 3-4-5 right triangle with lengths of 42-56-70? Thank you for the added explanation.


If it's 42-56-70, what is x then? Also, we get that BC, the smallest side, is \(35\sqrt{3}\) not 42.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128977 [0], given: 12185

Manager
Manager
User avatar
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 155

Kudos [?]: 137 [0], given: 39

Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 20 Sep 2014, 01:55
sarb wrote:
A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

(A) 35
(B) 42
(C) \(35\sqrt{3}\)
(D) \(7 + 35\sqrt{3}\)
(E) \(7 + 42\sqrt{3}\)



sin x = opp side/hypotenuse side

sin 60 =root(3)/2= x/70

x= 35 * root(3)

total height = 35 root (3)+ 7

:twisted: :twisted: :twisted: :twisted: :twisted:

Kudos [?]: 137 [0], given: 39

Intern
Intern
User avatar
Joined: 17 May 2012
Posts: 46

Kudos [?]: 12 [0], given: 126

A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 24 Mar 2015, 23:43
Hi All,

Another approach to solve this question is if you know the values of sin/cos angles. In this case sin 60 = Perpendicular/Hypotenuse i.e. sin 60 = BC/AB.
As sin 60 =\(\sqrt{3}/2\), we get \(\sqrt{3}/2\) = BC/70, thus BC = 35\(\sqrt{3}\)

From that you can get total height from the base 7 + 35\(\sqrt{3}\) as the final answer. Hope that helps.
Attachments

File comment: Trigonometry angles
trigonometry-angles4.jpg
trigonometry-angles4.jpg [ 7.53 KiB | Viewed 16461 times ]

Kudos [?]: 12 [0], given: 126

Manager
Manager
User avatar
Joined: 05 Jul 2015
Posts: 107

Kudos [?]: 27 [0], given: 3

Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 02 Nov 2015, 09:45
Bunuel wrote:
Notice that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

sarb wrote:
A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many meet above the ground does the ladder reach?

A. 35
B. 42
C. 35 root 3
D. 7 + 35 root 3
E. 7 + 42 root 3


Look at the diagram below:
Attachment:
Ladder.png
Triangle ABC is a 30°-60°-90° triangle. Now, in a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\), the leg opposite 30° (AC) corresponds with \(1\), the leg opposite 60° (BC) corresponds with \(\sqrt{3}\) and the hypotenuse AC corresponds with 2. So, \(\frac{BC}{AB}=\frac{\sqrt{3}}{2}\) --> \(\frac{BC}{70}=\frac{\sqrt{3}}{2}\) --> \(BC=35\sqrt{3}\).

Hence the leader reaches \(7+35\sqrt{3}\) above the ground.

Answer: D.


--------------------------------------------------------------------------------------------------------------

I understand this but I drew it sideways and got the answer of (B) 42

I'm not sure how you determined which side is the truck and which is the wall. Couldn't it have been a very long truck and a short wall that the ladder was against?

Kudos [?]: 27 [0], given: 3

Expert Post
3 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 836 [3], given: 5

Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 07 Jun 2016, 11:07
3
This post received
KUDOS
Expert's post
sarb wrote:
A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

(A) 35
(B) 42
(C) \(35\sqrt{3}\)
(D) \(7 + 35\sqrt{3}\)
(E) \(7 + 42\sqrt{3}\)


We are given that the ladder of a fire truck is elevated to an angle 60 degrees above the ground and that the ladder has a length of 70 feet. We are also given that the ladder is 7 feet above the ground. The best thing to do in this situation is to draw a diagram.

Image

Notice that the resulting triangle in the sketch is a 30-60-90 right triangle. Based on the given info, we don’t know that the ladder is leaning against a building whose side is perpendicular to the ground. The ratio of the sides of a 30-60-90 right triangle is x : x√3 : 2x. We see that the hypotenuse length of 70 feet is equal to the "2x" from the 30-60-90 ratio. Thus, we can set up an equation and solve for x.

70 = 2x

x = 35

Because x = 35, we know that the side opposite the 60-degree angle or, in this case, the height of the ladder, is 35√3. The height of the ladder is 35√3 feet and the base of the ladder is 7 feet above the ground; thus, we know that the ladder reaches a total height above the ground of 35√3 + 7 feet.

Answer D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 836 [3], given: 5

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16634

Kudos [?]: 273 [0], given: 0

Premium Member
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

Show Tags

New post 04 Jul 2017, 06:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Re: A ladder of a fire truck is elevated to an angle of 60° and   [#permalink] 04 Jul 2017, 06:17
Display posts from previous: Sort by

A ladder of a fire truck is elevated to an angle of 60° and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.