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

m∠a is 90°

m∠b is 40°

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true