SOLUTION: If the distance between the point at which a kite is held and the point at which it is directly overhead is 60 feet, and 100 feet of string has been let out, how far above the grou

Algebra ->  Pythagorean-theorem -> SOLUTION: If the distance between the point at which a kite is held and the point at which it is directly overhead is 60 feet, and 100 feet of string has been let out, how far above the grou      Log On


   

Question 249133: If the distance between the point at which a kite is held and the point at which it is directly overhead is 60 feet, and 100 feet of string has been let out, how far above the ground is the kite? (pythagorean theorem)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the string is the hypotenuse of the right triangle.
the point which it is directly overhead forms the adjacent side of the angle of the triangle that you need.

you need to find the angle first and then you can find the height.

cosine (angle) = adjacent divided by hypotenuse.

let the angle be called A.

adjacent side is 60 feet (length on the ground from the point of the holding of the kite to the point just underneath the kite.

hypotenuse side is 100 feet (length of the string holding the kite).

cosine (A) = 60/100 = .6

look up in the cosine tables to find that arccosine(.6) = 53.13010235 deegrees.

arccosine (x) means the angle whose cosine is x.

In this case we solved for arcosine (.6) to get our answer.

now that we know what the angle is, we can solve for the opposite side of the angle to get the height.

we can use either of 2 equations.

sine (53.13010235) = opposite / hypotenuse = x/100

tangent (53.13010235) = opposite / adjacent = x/60

both equations will lead to the same answer.

solving for x, first equation becomes

x = 100 * sine (53.13010235) = 80 feet.

x = 60 * tangent (53.13010235) = 80 feet.

your triangle looks like this: 

                       (C)  x
                            x  x
                            x     x    100
                            x        x
                            x           x
                            x              x  
                       (B)  x  x  x  x  x  x  x  (A)
                                     60

The triangle is ABC
The right angle is CBA
The person holding the string is at A.
Point B is directly beneath the kite.
Point C is the kite.
The line AC is the string
The line BA is the distance from the person holding the string to the point directly underneath the kite.
The angle you need to find is angle A, otherwise known as angle CAB.