In the triangle, is y = 30, then x =

Question

https://gmatclub.com/forum/download/file.php?id=41489 In the triangle, is y = 30, then x = A. 3 B. 4 C. 5 D. 8 E. 9 triangle.jpg

EgmatQuantExpert · Answer

Solution

Given:  
• In the triangle, angle y = 30

To find:  
• The value of x

Approach and Working:   
• As y = 30 and the other angle is 90, it is a 30-60-90 triangle
• We know, in a 30-60-90 triangle, the sides opposite to those respective angles are in the ratio  1: \sqrt{3}: 2 
• Hence, we can say  \frac{(2x – 3)}{(x + 6)} = \frac{1}{2} 
 Solving, 4x – 6 = x + 6
Or, 3x = 12
Or, x = 4

Hence, the correct answer is option B.

Answer: B

zishu912 · Answer

The right angle triangle is 30-60-90 traingle therefore the ratio of the side of the triangle = perpendicular:hypotenuse:base =1:2:sqrt(3)

so x + 6 = 2(2x-3) 
==>x + 6 = 4x - 6
==> 3x = 12
==> x = 4

Hence the correct answer will be option B

rahul2013 · Answer

sin30 degree = 1/2 =(2x-3)/(x+6)
After solving, we get x= 4 
So Ans - B

LipiSinha · Answer

if y=30 degree, then the given triangle is a 30-60-90 triangle. Hence, the sides will be in the raio 1:\sqrt{3}:2

Therefore, x+6 = 2(2x-3)
 x+6 = 4x-6
On solving, x=4. Hence, answer is B.

This can also be solved by substituting the answer choices.

x 2x-3 x+6
3 3 9
4 5 10
5 7 11
8 13 14
9 15 15

Now, according to the side ratio of a 30-60-90 triangle, x+6 must be the double of 2x-3 and only option  B  satisfies this condition.

In the triangle, is y = 30, then x =

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In the triangle, is y = 30, then x =

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