It is currently 19 Nov 2017, 00:07

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

Two sides of a triangle and their included angles are 4cm, 5cm and 30d

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

Hide Tags

Manager
Manager
User avatar
Joined: 25 Jan 2010
Posts: 109

Kudos [?]: 238 [0], given: 40

Location: Calicut, India
Two sides of a triangle and their included angles are 4cm, 5cm and 30d [#permalink]

Show Tags

New post 19 Nov 2011, 08:12
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (01:12) correct 38% (00:40) wrong based on 26 sessions

HideShow timer Statistics

Two sides of a triangle and their included angles are 4cm, 5cm and 30 degree resp. What is the are

A 10
B 15
C 5
D 20
[Reveal] Spoiler: OA

_________________

If u think this post is useful plz feed me with a kudo

Kudos [?]: 238 [0], given: 40

Expert Post
1 KUDOS received
GMAT Tutor
avatar
B
Joined: 24 Jun 2008
Posts: 1339

Kudos [?]: 1997 [1], given: 6

Re: Two sides of a triangle and their included angles are 4cm, 5cm and 30d [#permalink]

Show Tags

New post 21 Nov 2011, 08:56
1
This post received
KUDOS
Expert's post
cleetus wrote:
Two sides of a triangle and their included angles are 4cm, 5cm and 30degree resp. What is the are

A 10 B 15 C 5 D 20


Take the side of length 5 as your base. When you draw a height using this base, you will get a 30-60-90 triangle with a hypotenuse of 4. Since the short side in this triangle is our height, and since the short side in a 30-60-90 triangle is half the hypotenuse, the height is 2. So the area is 5*2/2 = 5.

A bit easier to see with a diagram of course.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 1997 [1], given: 6

Senior Manager
Senior Manager
User avatar
G
Joined: 02 Jul 2017
Posts: 269

Kudos [?]: 80 [0], given: 65

Location: India
GMAT ToolKit User CAT Tests
Re: Two sides of a triangle and their included angles are 4cm, 5cm and 30d [#permalink]

Show Tags

New post 11 Sep 2017, 10:48
Two sides of a triangle and their included angles are 4cm, 5cm and 30 degree resp. What is the area.

Please check attached image for detailed figure and explanation (ignore my handwriting :P)

Option 1: If we see 5 and 4 as sides, we usually go with right triangle and find 3rd side with Pythagoras theorem.
so 3rd side here = 3 . And area becomes 1/2 *4*3 =6
But its wrong answer as for right triangle 3,4,5 the angle between sides 5 and 4 is not 30 degree.
(Here non of the option is 6 so most likely we will not make this mistake)

Option 2: (Check attached img for diagram)
If we consider 5cm as base, we can draw a triangle using 4cm as 1 side and angle 30degree between them .
To find height of triamgle, drop perpendicular from 4cm side on 5cm base. Height can be calculated as we know angle = 30 degree.
So height = sin30 * 4cm = 2
so Area = 1/2 *5*2 = 5

Answer: C

Option 3: Using formula

Area formula if we know 2 sides of triangle and the angle between them =>

\(Area = \frac{a*b* Sin C}{2}\)
\(Area =\frac{4*5*Sin30}{2}\)

Area = 4*5*(1/2) /2 = 5

Answer: C

Attachments

Triangel with sides and angle.jpg
Triangel with sides and angle.jpg [ 1.63 MiB | Viewed 141 times ]

Kudos [?]: 80 [0], given: 65

Re: Two sides of a triangle and their included angles are 4cm, 5cm and 30d   [#permalink] 11 Sep 2017, 10:48
Display posts from previous: Sort by

Two sides of a triangle and their included angles are 4cm, 5cm and 30d

  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®.