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# What is the value of x?

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Manager
Joined: 03 Mar 2018
Posts: 206
What is the value of x?  [#permalink]

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15 Mar 2018, 08:28
1
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Difficulty:

15% (low)

Question Stats:

80% (01:27) correct 20% (01:20) wrong based on 44 sessions

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What is the value of x?
Attachment:

Capture1.JPG [ 21.87 KiB | Viewed 657 times ]

(A) 1
(B) 4/3
(C) 3/2
(D) 5/4
(E) 5/2

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Joined: 02 Aug 2009
Posts: 7958
Re: What is the value of x?  [#permalink]

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15 Mar 2018, 08:43
1
1
itisSheldon wrote:
What is the value of x?
Attachment:
Capture1.JPG

(A) 1
(B) 4/3
(C) 3/2
(D) 5/4
(E) 5/2

It is 30-60-90 triangle...
corresponding sides ratio is $$1:\sqrt{3}:2$$...
$$\frac{opposite 30}{opposite 90} = \frac{1}{2} = \frac{x+1}{4x-3}$$..
$$4x-3=2x+2........2x=5.....x=\frac{5}{2}$$

E
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What is the value of x?  [#permalink]

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16 Aug 2019, 07:40
For geometry questions where triangles are involved is really important to know sen, cos and tg of 0º 30º,45º, 60º and 90º

Hereunder a rule to remember all of them by just learning the values for sen

sen0º=0 (easy to remember because both are 0)
sen30º=1/2
sen45º=((2)^1/2)/2
sen60º=((3)^1/2)/2
sen 90=1 (easy to remember)

so you just need to memorize by heart sen30º and sen60º. The others are easy to remember

Now let's find out cos. You don't need to memorize. Just make the opposite from sen to get cos

sen0º=cos90º
sen30º=cos60º
sen45º=cos45º
sen60º=cos30º
sen90º=cos0º

Easy to remember right?

Finally to do tg, you just need to divide sen/cos. Don't memorize any of the tg forumlas. Tg are barely needed and if you finally need it for a questions just do sen/cos

Let's solve the question now:

cos60º=1/2=(x+1)/4x-3;

4x-3=2x+2 --->2x=5---> x=5/2

OPTION E
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What is the value of x?  [#permalink]

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16 Aug 2019, 07:42
1
itisSheldon wrote:
What is the value of x?
Attachment:
Capture1.JPG

(A) 1
(B) 4/3
(C) 3/2
(D) 5/4
(E) 5/2

$$cos 60 = \frac{1}{2} = \frac{x+1}{4x-3}$$
4x -3 = 2 (x+1) = 2x + 2
2x = 5
$$x= \frac{5}{2}$$

IMO E
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What is the value of x?   [#permalink] 16 Aug 2019, 07:42
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