• Apr 2nd 2009, 02:54 PM
jepal
So this is basically the question

matt is flying his kite at the end of a 40 meters string. The string makes and angle of pi/4 with the ground. The wind speed increases, kite flies higher until the string makes an angle of pi/3 with the ground.

Question:

Determine an exact expression for the horizontal distance that the kite moves between the two positions.

So far I got this

X2=40
---
√2
X1=20

Now im just subtracting these two and I got this

40-20√2
-----------=the diference but my books answer is 20 (√2-1)
√2
I would like to know how the book got that answer, I think my answer just needs to be simplfy but I cant get the same answer. When i calulate both i get the same answer. Please help!! this is really bothering me!!!
• Apr 2nd 2009, 04:35 PM
skeeter
Quote:

Originally Posted by jepal
So this is basically the question

matt is flying his kite at the end of a 40 meters string. The string makes and angle of pi/4 with the ground. The wind speed increases, kite flies higher until the string makes an angle of pi/3 with the ground.

Question:

Determine an exact expression for the horizontal distance that the kite moves between the two positions.

40 meters, angle of 45 degrees ... horizontal distance = 40/√2 = 20√2

same 40 meters , angle of 60 degrees ... new horizontal distance = 20
(short leg is half the hypotenuse, right?)

20√2 - 20 = 20(√2 - 1)
• Apr 2nd 2009, 04:46 PM
jepal
Quote:

Originally Posted by skeeter
40 meters, angle of 45 degrees ... horizontal distance = 40/√2 = 20√2

same 40 meters , angle of 60 degrees ... new horizontal distance = 20
(short leg is half the hypotenuse, right?)

20√2 - 20 = 20(√2 - 1)

Thank you for the reply. I still dont understand how is this possible

40/√2 = 20√2. Please explain or can you point me to a website where they explain this. I really struggle with these radical stuff!! thank u again!
• Apr 2nd 2009, 05:17 PM
skeeter
Quote:

Originally Posted by jepal
Thank you for the reply. I still dont understand how is this possible

40/√2 = 20√2. Please explain or can you point me to a website where they explain this. I really struggle with these radical stuff!! thank u again!

this method is called rationalizing the denominator ...

$\frac{40}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{40 \sqrt{2}}{2} = 20 \sqrt{2}$
• Apr 2nd 2009, 05:20 PM
jepal
ok just to clarify when rationalizing the denomintor, do u multiply both numerator and denominator with the radical. Thank u so much
• Apr 2nd 2009, 05:22 PM
skeeter
Quote:

Originally Posted by jepal
ok just to clarify when rationalizing the denomintor, do u multiply both numerator and denominator with the radical. Thank u so much

both ... you're really multiplying by 1