A kite is tied to the ground. The rays from the sun hit the kite perpendicular to the kite string, casting a shadow of the kite on the ground. The coordinates in the diagram are given in feet. What is the distance from where the kite is tied to the shadow? The sun is located in the upper left corner. The point where the kite is tied in in the lower left on a line representing the ground. This point is labeled left parenthesis 0 comma 0 right parenthesis. The shadow of the kite is located in the lower right on the line representing the ground. The kite is located in the middle with a point labeled left parenthesis 3 comma 12 right parenthesis. A dashed line is drawn from the sun, through the kite, to the shadow. (1 point) Responses 51 ft 51 ft 36 ft 36 ft 103 ft 103 ft 12.75 ft
To find the distance from where the kite is tied to the shadow, we can use the Pythagorean theorem.
The distance from the sun to the kite is the hypotenuse of a right triangle formed by the dashed line, with the lengths of the other two sides being the length of the kite's shadow and the height of the kite.
Using the coordinates given, we can calculate the length of the kite's shadow. The x-coordinate of the kite is 3 and the x-coordinate of the shadow is 0, so the length of the shadow is 3 - 0 = 3 feet.
The distance from the sun to the kite is the same as the height of the kite, which is 12 feet.
Using the Pythagorean theorem, we have:
(distance from where kite is tied to shadow)^2 = (length of shadow)^2 + (height of kite)^2
(distance from where kite is tied to shadow)^2 = 3^2 + 12^2
(distance from where kite is tied to shadow)^2 = 9 + 144
(distance from where kite is tied to shadow)^2 = 153
distance from where kite is tied to shadow ≈ 12.37 feet
Therefore, the distance from where the kite is tied to the shadow is approximately 12.37 feet.