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

135 is your answer

step-by-step explanation:

try 180 times three then divide that number by 4 (sides) to get your answer. im glad to : )

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b