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 diagram shows the sun, kite, string, and shadow of the kite on the ground.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
36 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.
From the diagram, we can see that the height of the kite is 12 feet (the y-coordinate of the kite is 12).
The base of the right triangle formed by the dashed line, the kite string, and the shadow is the x-coordinate of the kite, which is 3 feet.
Using the Pythagorean theorem, we can find the length of the dashed line:
\(d^2 = 3^2 + 12^2\)
\(d^2 = 9 + 144\)
\(d^2 = 153\)
\(d = \sqrt{153}\)
\(d \approx 12.36\) feet
Therefore, the distance from where the kite is tied to the shadow is approximately 12.36 feet.