BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Geometry Triangle Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 78
Joined: Sun Nov 30, 2014 7:21 pm
Thanked: 1 times
Followed by:2 members

Geometry Triangle Problem

by me_1234 » Wed Dec 10, 2014 6:21 pm
A ladder of a fire truck is elevated to an angle of 60 degrees 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√3
D/ 7 + 35√3 (Correct Answer)
E/ 7 + 42√3

When I did this problem I did the following - can someone tell me where I went wrong?

Using the properties of a 30-60-90 triangle, I set up a ratio:

70 = 2
x √3

70 * √3 = 2x, then divide by 2:

35 * (√3/2) = x

So my answer was 7 + 35* (√3/2)
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 10, 2014 7:26 pm
melanie.espeland wrote:A ladder of a fire truck is elevated to an angle of 60 degrees 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√3
D/ 7 + 35√3 (Correct Answer)
E/ 7 + 42√3

When I did this problem I did the following - can someone tell me where I went wrong?

Using the properties of a 30-60-90 triangle, I set up a ratio:

70 = 2
x √3

70 * √3 = 2x, then divide by 2:

35 * (√3/2) = x

So my answer was 7 + 35* (√3/2)
You ALMOST had it.
Let's take it from:
70√3 = 2x
Divide both sides by 2 to get: 35√3 = x [not x = 35(√3/2)]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Senior | Next Rank: 100 Posts
Posts: 78
Joined: Sun Nov 30, 2014 7:21 pm
Thanked: 1 times
Followed by:2 members

by me_1234 » Wed Dec 10, 2014 8:29 pm
Hi Brent,

When you have 70 * √3 = 2x, then divide by 2, why isn't it 70/2 and √3/2? It looks like you are only dividing 70 by 2.

Thanks

Melanie
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 10, 2014 8:44 pm
melanie.espeland wrote:Hi Brent,

When you have 70 * √3 = 2x, then divide by 2, why isn't it 70/2 and √3/2? It looks like you are only dividing 70 by 2.

Thanks

Melanie
Let's examine an easier question:
How about (10)(4) = 2x
Would we divide the 10 AND the 4 by 2? No.
We take (10)(4) and divide by 2 to get: (10)(4)/2 = (2)(5)(4)/2 = (5)(4) = 20

Likewise, if 70√3 = 2x, then x = (70√3)/2 = (2)(35)(√3)/2 = (35)(√3)

Cheers,
Brent






Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Legendary Member
Posts: 2135
Joined: Mon Feb 03, 2014 9:26 am
Location: https://martymurraycoaching.com/
Thanked: 955 times
Followed by:140 members
GMAT Score:800

by MartyMurray » Wed Dec 10, 2014 9:21 pm
melanie.espeland wrote:Hi Brent,

When you have 70 * √3 = 2x, then divide by 2, why isn't it 70/2 and √3/2? It looks like you are only dividing 70 by 2.

Thanks

Melanie
That's right, Melanie. One does only divide the 70, or alternatively you divide the entire thing, (70 * √3), by 2. What you are doing is actually dividing twice. If the 70 * √3 were instead 70 + √3, THEN you would need to divide each of them, but since they are multiplied, you need to divide only once.

Here's another way to look at it.

The proportions of the sides of a 30 - 60 - 90 triangle are 1 : √3 : 2.

The hypotenuse is the 2, and in this case the hypotenuse has length 70. So to work with this triangle, let's divide the 70 by 2 to get our basic unit for the lengths of the sides, 70/2 = 35.

Now to get the lengths of the three sides, we can plug the 35 into the ratio to get 1(35) : √3(35) : 2(35).

The height above the ground is 7 + the length of that √3(35) side. So it's 7 + √3(35), or as they put it 7 + 35√3.
Top
Senior | Next Rank: 100 Posts
Posts: 78
Joined: Sun Nov 30, 2014 7:21 pm
Thanked: 1 times
Followed by:2 members

by me_1234 » Thu Dec 11, 2014 9:30 am
Thank you Brent and Marty, totally get it now.
Top
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 am
Thanked: 25 times
Followed by:1 members

by Mathsbuddy » Fri Dec 19, 2014 6:25 am
Height, h = 7 + 70sin60(degrees)
but sin60 = SQRT[3/4]= SQRT[3]/2
So, h = 7 + 70 SQRT[3]/2 = 7 + 35 SQRT[3]
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Dec 19, 2014 8:19 am
Hi Mathsbuddy,

While using trigonometry to answer this question is one way to get to the solution, it's worth noting that NO GMAT questions will ever require you to use trigonometry to get to the solution.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sat Oct 26, 2019 9:13 am
me_1234 wrote:A ladder of a fire truck is elevated to an angle of 60 degrees 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√3
D/ 7 + 35√3 (Correct Answer)
E/ 7 + 42√3
Here's an idea of what's going on....
Image
When we compare the big triangle with the BASE 30-60-90 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√3
Image

Now 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...
Image

So, the TOTAL distance from the top of the ladder to the ground = 35√3 + 7

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1