Answer:
Step-by-step explanation:
1). Coordinates of Art → (1, -5).
Coordinates of Library → (1, 9)
Coordinates of Science → (-5, -5)
Distance between Art and Library =
=
= 14 units
Distance between Art and Science =
= 6 units
Since 14 > 6,
Art is closer to Science than Library.
Answer is False.
2). Coordinates of Cafeteria → (-7, 9)
True.
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 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 <u>Pithagorean theorem</u>:
(7)
Isolating and writing with the known values:
(8)
(9)
This is the distance between the kite and the house
