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Arada [10]
3 years ago
7

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 ?

Mathematics
1 answer:
fiasKO [112]3 years ago
3 0

Answer: 125.80 ft

Step-by-step explanation:

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

How?

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

For y:

sin(65 \°)=\frac{y}{45 ft} (1)

Where y is the opposite side to the angle and 45 ft the hypotenuse.

Isolating y:

y=40.78 ft (2)

For x:

cos(65 \°)=\frac{x}{45 ft} (3)

Where x is the adjacent side to the angle.

Isolating x:

y=19.017 ft (4)

Finding d:

d=x+100 ft (5)

d=19.017 ft +100 ft

d=119.017 ft (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 h and the sides are the values calculated in (4) and (6).

So, in this case we will use the <u>Pithagorean theorem</u>:

h^{2}=y^{2} +d^{2} (7)

Isolating h and writing with the known values:

h=\sqrt{y^{2} +d^{2}} (8)

h=\sqrt{(19.017 ft)^{2} +(119.017 ft)^{2}} (9)

h=125.80 ft This is the distance between the kite and the house

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