SOLUTION: A kite flying 20 ft. above the ground is attached to a string 80 ft. long. The string is being held by a person on the ground.if the kite fell vertically to the ground, how far aw

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Question 437230: A kite flying 20 ft. above the ground is attached to a string 80 ft. long. The string is being held by a person on the ground.if the kite fell vertically to the ground, how far away from the stake would the kite land?
Found 3 solutions by mananth, ikleyn, greenestamps:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
sin theta = vertical/hypotenuse
Sinetheta = 20/80
Sinetheta= 1/4
Theta=15 deg
..
Cos theta = base/hyptenuse
Cos 15* 80 = base
0.9659*80= 77 feet ground distance (approx)

Answer by ikleyn(53426) About Me  (Show Source):
You can put this solution on YOUR website!
.
A kite flying 20 ft. above the ground is attached to a string 80 ft. long.
The string is being held by a person on the ground. if the kite fell vertically to the ground,
how far away from the stake would the kite land?
~~~~~~~~~~~~~~~~~~~~


In his solution, @mananth uses this scheme 

    Find sin of the angle --->  find arcsin  --->  find cos --->  find the horizontal distance.

In this scheme, one step is excessive.

The better scheme is 

    find sin(a)  --->  find cos(a) = sqrt%281-sin%5E2%28a%29%29  --->  find the horizontal distance.


I will use this improved scheme in my calculation


        (1)   Find  sin(a)  of angle of depression   sin(a) = 20%2F80 = 1%2F4.

        (2)   Find  cos(a) = sqrt%281+-+sin%5E2%28a%29%29 = sqrt%281+-+%281%2F4%29%5E2%29 = 0.968245837.

        (3)   Horizontal distance = 80*cos(a) = 80*0.968245837 = 77.46 ft  (approximately).         ANSWER


It is how this problem IS EXPECTED to be solved.



Answer by greenestamps(13258) About Me  (Show Source):
You can put this solution on YOUR website!


The use of trigonometry to solve the problem is a bit excessive -- unless a solution using trigonometry is required....

The problem simply involves a right triangle with hypotenuse 80 and one leg 20. The answer to the question is the length of the other leg, which can be found using the Pythagorean Theorem.

x%5E2%2B20%5E2=80%5E2
x%5E2%2B400=6400
x%5E2=6000

Use a calculator to find...

ANSWER: (to 2 decimal places) 77.46 feet