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# In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l

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Joined: 02 Nov 2016
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In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 03:22
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45% (medium)

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67% (02:30) correct 33% (02:33) wrong based on 21 sessions

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In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the length of ST ?

A. 6
B. 12
C. 24
D. 36
E. 72

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Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 03:57
1
Attachment:
NJNJ.jpg

In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the length of ST ?

A. 6
B. 12
C. 24
D. 36
E. 72

IMO B

This means side ST will be the greatest side among all.

SR = 6$$\sqrt{2}$$ = 6*1.414 ~ 9

RT = 6($$\sqrt{3}$$ - 1) ~ 4

No ideally it can be 12, 9+4 > 12 & 5 < 12
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Joined: 18 Dec 2018
Posts: 2
Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 07:23
The value should be between the sum of the two sides and their difference. So in between 6 and 19. Only 12 fits in this category. Hence option B

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Director
Status: Manager
Joined: 27 Oct 2018
Posts: 689
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 08:02
The value should be between the sum of the two sides and their difference. So in between 6 and 19. Only 12 fits in this category. Hence option B

Posted from my mobile device

$$6\sqrt[]{2} = 6*1.4 = 8.4$$
$$6 (\sqrt[]{3}-1) = 6*(1.7-1) = 6*0.7 = 4.2$$

so the range is between 12.6 and 4.2

how come 6 and 19?
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Director
Status: Manager
Joined: 27 Oct 2018
Posts: 689
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 08:09
1
by extending RT to form the right angle triangle TZS,

ZSR is a 45:45:90 triangle with side ratios of $$1:1:\sqrt{2}$$
so SZ = 6

and SZT is a 30:60:90 triangle with side ratios of $$1:\sqrt{3}:2$$
so ST = 12

B
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Intern
Joined: 18 Dec 2018
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Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 08:17
1
Mahmoudfawzy83 wrote:
The value should be between the sum of the two sides and their difference. So in between 6 and 19. Only 12 fits in this category. Hence option B

Posted from my mobile device

$$6\sqrt[]{2} = 6*1.4 = 8.4$$
$$6 (\sqrt[]{3}-1) = 6*(1.7-1) = 6*0.7 = 4.2$$

so the range is between 12.6 and 4.2

how come 6 and 19?
My bad. But we can eliminate 6 as the side opposite to the largest angle is the longest.
Director
Joined: 27 May 2012
Posts: 905
Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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05 Mar 2019, 20:11
Attachment:
NJNJ.jpg

In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the length of ST ?

A. 6
B. 12
C. 24
D. 36
E. 72

Actually answer is B, we can extend side RT to form a right triangle having angles ,90 45 45.

You may want to check out this post.
https://gmatclub.com/forum/in-triangle- ... l#p2223923
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- Stne
Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l   [#permalink] 05 Mar 2019, 20:11
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