Kite Distance Above the Ground

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Discussion Overview

The discussion revolves around calculating the height of a kite above the ground based on the length of the string and the angle it makes with the ground. Participants explore the use of the sine function in this context, discussing potential errors in calculations related to calculator settings.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Kaila proposes using the sine function to find the height of the kite, setting up the equation sin(70°) = h/65.
  • Some participants question whether calculators are set to degree mode, suggesting it may affect the results.
  • One participant claims to have calculated the height as approximately 50 meters, while another states a different value of 27 meters based on their evaluation.
  • There are multiple requests for participants to show their calculations to clarify discrepancies in results.
  • Participants acknowledge that the expression for height is correct, but there are differences in numerical evaluations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct height of the kite, as differing numerical evaluations persist. There is also uncertainty regarding the mode of calculators used by participants.

Contextual Notes

Limitations include potential misunderstandings about calculator settings (degree vs. radians) and the accuracy of numerical evaluations based on those settings.

xyz_1965
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Kaila is flying a kite whose string is making a 70° angle with the ground. The kite string is 65 meters long. How far is the kite above the ground?

I am thinking the sine function.

sin (70°) = h/65, where h is the distance of the kite above the ground.

sin (70°)(65) = h

27.08617 = h

I will say the kite is 27 meters above the ground.
 
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Do you have your calculator in degree mode?
 
MarkFL said:
Do you have your calculator in degree mode?

Yes, my calculator is in degree mode. Should it be in radians mode?
 
Try evaluating the expression again...
 
MarkFL said:
Try evaluating the expression again...

sin (70°)(65) = 50.3028943013 in radians mode.

I say the answer is 50 meters.
 
I'm getting a different number.
 
MarkFL said:
I'm getting a different number.

What number are you getting? Show me your set up.
 
xyz_1965 said:
What number are you getting? Show me your set up.

Your expression is correct, but your numeric evaluation of that expression differs from mine.
 
MarkFL said:
Your expression is correct, but your numeric evaluation of that expression differs from mine.

Show me what you did.
 
  • #10
xyz_1965 said:
Show me what you did.

I used my phone's calculator.
 
  • #11
65sin(70).png
 
  • #12
skeeter said:
https://www.physicsforums.com/attachments/10524

That looks like what I got.
 
  • #13
xyz_1965 said:
sin (70°)(65) = 50.3028943013 in radians mode.

I say the answer is 50 meters.

your argument for sine is 70 degrees ... you need to be in degree mode.
 
  • #14
skeeter said:
your argument for sine is 70 degrees ... you need to be in degree mode.

Understood.
 
  • #15
MarkFL said:
That looks like what I got.

I must be in degree mode. I got it.
 
  • #16
MarkFL said:
I used my phone's calculator.

Your phone in degree mode, right?
 
  • #17
xyz_1965 said:
Your phone in degree mode, right?

It appears to be by default.
 
  • #18
MarkFL said:
It appears to be by default.

Moving on.
 
  • #19
Ha! Ha!
 

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