Question

kyle is pulled back on a swing so that the rope forms an angle of 30 degrees with the vertical. the distance from the top of the swing set directly to the ground is 12 feet. find kyles height off the ground, x, when he is in the pulled back position. round the answer to the nearest hundredth.
a. 3.34 feet
b. 3.86 feet
c. 8.56 feet
d. 8.66 feet

Answer 1

@pitamar

Answer 2

Ok, do you know trigonometry?

Answer 3

nope

Answer 4

How about 30-60-90 triangles?

Answer 5

heard of it but dont rememeber

Answer 6

Let me find a nice picture

Answer 7

http://mathworld.wolfram.com/images/eps-gif/30-60-90Triangle_1000.gif

Answer 8

you can see that the side in front of the \(30^\circ\) angle is always half the hypotenuse
The side in front of the \(60^\circ\) angle is always \(\frac{\sqrt{3}}{2}\) of the hypotenuse. A little ugly I know.

Answer 9

yea lol

Answer 10

Ok so let me draw it

Answer 11

First, we need to find the hypotenuse, which is the length of the rope.
For that we are told that the height of the top of the swing is 12ft and from the drawing we know that the swing is idle it is at height of 2ft. So what is the length of the rope?

Answer 12

30 degrees

Answer 13

we know that the row length + 2ft is total of 12ft.
x + 2 = 12
what is x?

Answer 14

10

Answer 15

exactly. so let's put it in the drawing:

Answer 16

Now we have to find the height of the swing. So first let's find how high above it the tip is: