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

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

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New post 10 Feb 2019, 03:22
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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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Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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New post 10 Feb 2019, 03:57
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SajjadAhmad wrote:
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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


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

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New post 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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Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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New post 10 Feb 2019, 08:02
priyadabas01 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

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

so the range is between 12.6 and 4.2

how come 6 and 19?
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In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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New post 10 Feb 2019, 08:09
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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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Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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New post 10 Feb 2019, 08:17
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Mahmoudfawzy83 wrote:
priyadabas01 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

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

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

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New post 05 Mar 2019, 20:11
SajjadAhmad wrote:
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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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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