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

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Senior RC Moderator
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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, 04:55
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67% (01:56) correct 33% (02:54) wrong based on 9 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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Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 06:23
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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10 Feb 2019, 07:02
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

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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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Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 155
Location: Malaysia
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, 07:09
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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Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l  [#permalink]

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10 Feb 2019, 07:17
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.
Re: In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l   [#permalink] 10 Feb 2019, 07:17
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