It is currently 18 Jan 2018, 19:56

### 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

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

# 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

Intern
Joined: 12 May 2012
Posts: 25

Kudos [?]: 214 [6], 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

07 Jun 2012, 00:16
6
KUDOS
23
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:22) correct 20% (01:40) wrong based on 1282 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, 04:04, edited 1 time in total.
Edited the question.

Kudos [?]: 214 [6], given: 19

Intern
Status: ISB 14...:)
Joined: 25 May 2012
Posts: 30

Kudos [?]: 43 [1], given: 11

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

### Show Tags

07 Jun 2012, 00:47
1
KUDOS
Vertical height of ladder = 70.sin(60) = 35root3

Total height = 7 + 35root3

Kudos [?]: 43 [1], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139442 [6], given: 12790

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

### Show Tags

07 Jun 2012, 10:50
6
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:

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 AB 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.

For more check Triangles chapter of Math Book: http://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.

[Reveal] Spoiler:
Attachment:

Ladder.png [ 5.44 KiB | Viewed 34200 times ]

_________________

Kudos [?]: 139442 [6], given: 12790

Intern
Joined: 12 May 2012
Posts: 25

Kudos [?]: 214 [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

07 Jun 2012, 18:21
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:
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.

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

Hope it helps.

Thank you that made it very simple

Kudos [?]: 214 [0], given: 19

VP
Joined: 08 Jun 2010
Posts: 1380

Kudos [?]: 176 [0], given: 916

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

### Show Tags

21 Feb 2013, 09:31
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 [?]: 176 [0], given: 916

Manager
Joined: 24 Sep 2012
Posts: 89

Kudos [?]: 177 [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

21 Feb 2013, 09:38
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 [?]: 177 [0], given: 3

Intern
Joined: 18 May 2013
Posts: 7

Kudos [?]: 10 [0], given: 55

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

### Show Tags

22 Jul 2013, 09:44
I do not get the ratio 1 : 2 : √3

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

Kudos [?]: 10 [0], given: 55

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139442 [2], given: 12790

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

### Show Tags

22 Jul 2013, 09:48
2
KUDOS
Expert's post
sv3n wrote:
I do not get the ratio 1 : 2 : √3

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

Check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
_________________

Kudos [?]: 139442 [2], given: 12790

Intern
Joined: 18 May 2013
Posts: 7

Kudos [?]: 10 [0], given: 55

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

### Show Tags

22 Jul 2013, 09:51
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?

Check Triangles chapter of Math Book: ...

Hope it helps.

OK.. IT´S GIVEN.

Thanks a lot!

Kudos [?]: 10 [0], given: 55

Intern
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

29 Dec 2013, 10:00
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

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139442 [0], given: 12790

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

### Show Tags

29 Dec 2013, 10:16
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.
_________________

Kudos [?]: 139442 [0], given: 12790

Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 152

Kudos [?]: 153 [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

20 Sep 2014, 00:55
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

Kudos [?]: 153 [0], given: 39

Intern
Joined: 17 May 2012
Posts: 44

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

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

### Show Tags

24 Mar 2015, 22:43
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 [ 7.53 KiB | Viewed 19938 times ]

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

Manager
Joined: 05 Jul 2015
Posts: 107

Kudos [?]: 28 [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

02 Nov 2015, 08:45
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:
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.

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

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 [?]: 28 [0], given: 3

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1820

Kudos [?]: 1048 [3], given: 5

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

### Show Tags

07 Jun 2016, 10:07
3
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.

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.

_________________

Jeffery Miller
Head of GMAT Instruction

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

Kudos [?]: 1048 [3], given: 5

Manager
Joined: 09 Mar 2016
Posts: 137

Kudos [?]: 24 [1], given: 190

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

### Show Tags

27 Nov 2017, 12:41
1
KUDOS
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:

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.

For more check Triangles chapter of Math Book: http://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.

Bunuel hello isn't a hypotenuse the longest one AB? why are you saying it is AC ? please explain have a great day ! D.

Kudos [?]: 24 [1], given: 190

Intern
Joined: 15 Nov 2017
Posts: 41

Kudos [?]: 13 [0], given: 10

Location: United States (OR)
Concentration: Marketing, Entrepreneurship
Schools: McCombs
GMAT 1: 630 Q40 V40
GPA: 2.99
WE: Education (Consulting)
Re: A ladder of a fire truck is elevated to an angle of 60° and [#permalink]

### Show Tags

27 Nov 2017, 18:09
You have to assume the ladder is attached to the truck! That threw me off...
_________________

McCombs MBA 1990, Hook'Em Horns. I am helping my son prep for 2019, while trying to keep a 66 y.o. brain active.

Kudos [?]: 13 [0], given: 10

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139442 [0], given: 12790

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

### Show Tags

27 Nov 2017, 22:12
dave13 wrote:
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:

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.

For more check Triangles chapter of Math Book: http://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.

Bunuel hello isn't a hypotenuse the longest one AB? why are you saying it is AC ? please explain have a great day ! D.

There was a typo: AC instead of AB. Edited. Thank you.
_________________

Kudos [?]: 139442 [0], given: 12790

Re: A ladder of a fire truck is elevated to an angle of 60° and   [#permalink] 27 Nov 2017, 22:12
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

 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®.