Jack is flying his kite . He runs 100 feet away from his house and lets out 45 feet of string . The angle of elevation from the ground to the kite is 65 degrees . How far is the kite from the house ?

125.80 ft

Step-by-step explanation:

Asuming the described situation is as shown in the figure below, we need to find the distance between the kite and Jacks house, but first we need to find the , and then .

How?

We will use trigonometry, especifically the trigonometric functions sine and cosine:

For :

(1)

Where is the opposite side to the angle and the hypotenuse.

Isolating :

(2)

For :

(3)

Where is the adjacent side to the angle.

Isolating :

(4)

Finding :

(5)

(6)

Now that we have found these values, we have to work with a bigger triangle, where the hypotenuse is the distance between the kite and Jack's house and the sides are the values calculated in (4) and (6).

So, in this case we will use the Pithagorean theorem:

(7)

Isolating and writing with the known values:

(8)

(9)

This is the distance between the kite and the house

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation:

ok thats very interesting