Jun 29 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jun 30 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Jul 01 08:00 AM PDT  09:00 AM PDT Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Jul 01 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 12 May 2012
Posts: 18
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:
81% (01:48) correct 19% (02:14) wrong based on 1623 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: 55801

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 58223 times ]
_________________




Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



CEO
Joined: 12 Sep 2015
Posts: 3787
Location: Canada

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
07 Sep 2018, 14:15
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) \(7 + 42\sqrt{3}\) Here's an idea of what's going on.... When we compare the big triangle with the BASE 306090 special triangle (which you must memorize for test day!), we can see that the hypotenuse of the big triangle is 35 times as long as the hypotenuse of the base triangle. This means the big triangle is 35 times the size of the base triangle. This means that, on the big triangle, the side opposite the 60 degree angle must be 35√3Now before we (incorrectly) choose answer choice C, we must keep in mind that the question tells us the base of the ladder is 7 feet above the ground... So, the TOTAL distance from the top of the ladder to the ground = 35√3 + 7Answer: D Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Math Expert
Joined: 02 Sep 2009
Posts: 55801

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
22 Jul 2013, 10:48
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: mathtriangles87197.htmlHope it helps.
_________________



Intern
Status: ISB 14...:)
Joined: 26 May 2012
Posts: 28
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



Manager
Joined: 24 Sep 2012
Posts: 83
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.



VP
Joined: 09 Mar 2016
Posts: 1274

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.



Intern
Joined: 12 May 2012
Posts: 18
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



Director
Joined: 09 Jun 2010
Posts: 775

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.



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!



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: 55801

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
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 345 right triangle with lengths of 425670? Thank you for the added explanation. If it's 425670, what is x then? Also, we get that BC, the smallest side, is \(35\sqrt{3}\) not 42. Hope it's clear.
_________________



Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 129
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: 35

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 40058 times ]



Manager
Joined: 05 Jul 2015
Posts: 97
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?



Math Expert
Joined: 02 Sep 2009
Posts: 55801

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.
_________________



Intern
Joined: 15 Sep 2018
Posts: 3

Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
Show Tags
23 Mar 2019, 21:52
How do i know this is a 603090 triangle and not 606060?
Posted from my mobile device




Re: A ladder of a fire truck is elevated to an angle of 60° and
[#permalink]
23 Mar 2019, 21:52



Go to page
1 2
Next
[ 23 posts ]



