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!!!

2. 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)

3. 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!

4. 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 ...

$\frac{40}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{40 \sqrt{2}}{2} = 20 \sqrt{2}$

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

6. 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