Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 12 May 2012
Posts: 24
Location: United States
Concentration: Technology, Human Resources

A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
Updated on: 07 Dec 2012, 05:04
Question Stats:
79% (01:22) correct 21% (01:40) wrong based on 1529 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) \(7 + 42\sqrt{3}\)
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by sarb on 07 Jun 2012, 01:16.
Last edited by Bunuel on 07 Dec 2012, 05:04, edited 1 time in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 47200

A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
07 Jun 2012, 11:50
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. Answer: D. For more check Triangles chapter of Math Book: http://gmatclub.com/forum/mathtriangles87197.htmlHope it helps. Attachment:
Ladder.png [ 5.44 KiB  Viewed 43719 times ]
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Intern
Status: ISB 14...:)
Joined: 26 May 2012
Posts: 29
Location: India
Concentration: Strategy
GPA: 3.62
WE: Engineering (Energy and Utilities)

Re: maths problem
[#permalink]
Show Tags
07 Jun 2012, 01:47
Vertical height of ladder = 70.sin(60) = 35root3
Total height = 7 + 35root3



Intern
Joined: 12 May 2012
Posts: 24
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, 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: mathtriangles87197.htmlHope it helps. Thank you that made it very simple



VP
Joined: 09 Jun 2010
Posts: 1165

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



Manager
Joined: 24 Sep 2012
Posts: 85
Location: United States
Concentration: Entrepreneurship, International Business
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, 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.



Intern
Joined: 18 May 2013
Posts: 7
Location: Germany
GMAT Date: 09272013

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



Math Expert
Joined: 02 Sep 2009
Posts: 47200

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
22 Jul 2013, 10:48



Intern
Joined: 18 May 2013
Posts: 7
Location: Germany
GMAT Date: 09272013

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
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. Thanks a lot!



Intern
Joined: 03 Aug 2013
Posts: 1

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
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 345 right triangle with lengths of 425670? Thank you for the added explanation.



Math Expert
Joined: 02 Sep 2009
Posts: 47200

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
29 Dec 2013, 11:16



Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 146
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, 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



Intern
Joined: 17 May 2012
Posts: 41

A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
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
trigonometryangles4.jpg [ 7.53 KiB  Viewed 27436 times ]



Manager
Joined: 05 Jul 2015
Posts: 104
Concentration: Real Estate, International Business
GPA: 3.3

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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
07 Jun 2016, 11:07
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 306090 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 306090 right triangle is x : x√3 : 2x. We see that the hypotenuse length of 70 feet is equal to the "2x" from the 306090 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 60degree 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 SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 09 Mar 2016
Posts: 661

A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
27 Nov 2017, 13:41
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. Answer: D. For more check Triangles chapter of Math Book: http://gmatclub.com/forum/mathtriangles87197.htmlHope 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.



Intern
Joined: 15 Nov 2017
Posts: 41
Location: United States (OR)
Concentration: Marketing, Entrepreneurship
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, 19:09
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.



Math Expert
Joined: 02 Sep 2009
Posts: 47200

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
27 Nov 2017, 23:12
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. Answer: D. For more check Triangles chapter of Math Book: http://gmatclub.com/forum/mathtriangles87197.htmlHope 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.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Re: A ladder of a fire truck is elevated to an angle of 60° and &nbs
[#permalink]
27 Nov 2017, 23:12






