Geometry

Question

Try this one on.

IrinaOK · Answer

I get sqrt(3)

Is it something else?

bkk145 · Answer

1 is the answer

For the triangle to your left, you have 30-60-90 triangle. Therefore, you know that the radius of the circle is 2 using its relationship. This is obvious.

For the triangle to your right, you can get the angle at the origin because you know a straight line is 180. So, 180-30-90 = 60. Work out the relationship, you get S=1

IrinaOK · Answer

Where is exactly --30-60-90--- triangle?
All triangles I see are 90:45:45....

please, tell if I am missing something,,,

aren`t the two triangles simetrical, anyways?

bkk145 · Answer

no, two triangles are not symmetrical, that's a trap! :D

For the triangle on your left, you have point P = (x,y) = (-sqrt(3),1)
If you draw a line from point P coming down to perpendicular with x coordinate, you'll have yourself a triangle with x coordinate side = sqrt(3) and y coordinate side = 1, which implies 30-60-90 triangle.

IrinaOK · Answer

I got it !!

Two radius devide 180 degrees as 30:90:60!! Wrong assumptions... good one

Thank you.

Whatever · Answer

1 is the answer.

If I see 1, sqrt3 --> 30-60-90. The rest is a peace of cake.

ggarr · Answer

ok. I got the 30-60-90 relationship on the left side. I'm having trouble w/the rhs. I'm assuming we can draw a perpendicular line from point Q to the x coordinate and create a triangle similar to the one on the lhs. once I do this, I'm lost. Earlier it was mentioned that 180 - 90 - 30 = 60. I understand that a straight line is 180. But what made you subtract 90 and 30 from 180 to get 60? does 90 degrees come from the 90 degree angle formed when point Q is connected to the x coordinate? if so, where does 60 degrees come from?

bkk145 · Answer

Angle POA=30, POQ=90
Did you get this?
If so, the x coordinate is just a line of 180 degree and you know that
POA + POQ + QOX = 180
Therefore, QOX = 180 - 90 - 30 = 60

ywilfred · Answer

Length of OP = sqrt((sqrt3)^2 + (1)^2) = 2
OQ^2 = 4 = s^2 + t^2 ---  

Since OP = OQ and <O = 90 degrees, so we have ourselves a 45-45-90 triangle.

So PQ = 2sqrt2

(2sqrt2)^2 = (s+sqrt(3))^2 + (t-1)^2
8 = s^2 + 2s(sqrt3) + 3 + t^2 - 2t + 1
2s(sqrt3) -2t = 0
s(sqrt3) = t
t^2 = 3s^2 ---  

substitute   to p1[

4s^2 = 4
s^2 = 1
s = 1 (-1 is not valid since s is on the postive side of the x-axis)

Ferihere · Answer

If somebody doesnot understand I would suggest to use very basic trigonometry, about right triangle and finding angles by using info about two sides. sin, cos, tan and cotan. 

It is very easy digest, and you will see where 60 degrees on right triangle came from.

 Ans: 1

zion · Answer

I am having trouble understanding why you guys are talking about traingle right to y-axis, and triangle left to the y-axis. The only traingle i could see is a 45-45-90 and. Since rest of the diagram is not drawn to the scale, how can assume things like that. The only to solve this as i could see is by solving the equations.

Can you please explain the basic trigonometry you applied to solve the problem.

zion · Answer

My Bad, i could the the 30-60-90 traingles, but dont think necessary to go through trigonometry.

By the way, do we really need to study the trigonometry to go through the quant.

ggarr · Answer

no, two triangles are not symmetrical, that's a trap!

For the triangle on your left, you have point P = (x,y) = (-sqrt(3),1) If you draw a line from point P coming down to perpendicular with x coordinate, you'll have yourself a triangle with x coordinate side = sqrt(3) and y coordinate side = 1, which implies 30-60-90 triangle. ok. I got the 30-60-90 relationship on the left side. I'm having trouble w/the rhs. I'm assuming we can draw a perpendicular line from point Q to the x coordinate and create a triangle similar to the one on the lhs. once I do this, I'm lost. Earlier it was mentioned that 180 - 90 - 30 = 60. I understand that a straight line is 180. But what made you subtract 90 and 30 from 180 to get 60? does 90 degrees come from the 90 degree angle formed when point Q is connected to the x coordinate? if so, where does 60 degrees come from? Angle POA=30, POQ=90 Did you get this? If so, the x coordinate is just a line of 180 degree and you know that POA + POQ + QOX = 180 Therefore, QOX = 180 - 90 - 30 = 60 Gotcha. Thanks. I really should have seen that.

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