Child's Play-How high was the swing?

[Medgirl314]

Homework Statement

A swing is on a rope that is 3.0 m long. The swing is 1.1 meters above the ground at its lowest point. Find its height above the ground when the rope makes an angle of 34 degrees with the vertical.

Homework Equations

tan=opp/adj

The Attempt at a Solution

tan=opp/adj

tan(34)=3.0/1.1
Height=1.84 m

This seems slightly off, but mostly right. Does anyone have any critiques?

Thanks in advance!

 

[Konoha]

Try to draw the swing in it's lowest position and the 34 degree, this way you can easily find opposite, adjacent and hypotenuse.
and why didn't use Cos(34). If you draw it, you can see it makes more sense to use cosine here.

 

[Medgirl314]

Ah, okay. Believe it or not, I have a diagram. xD I just couldn't decide which was which because it doesn't have a right angle.

Trying cosine:

cos(34)*3.0/1.1=2.26 m.

How's that? Thank you!

 

[Konoha]

:) It's alright. Try drawing a straight line from the 34 degree position, perpendicular to the line marking the lowest position. Now you should have a triangle, with the 34 degree angle on top, a right angle in bottom left.
Let me know how it goes.

 

[Medgirl314]

I'm sorry! For whatever reason I didn't get a notification that you posted here. I think I figured it out. I turned it in and didn't do as well as I hoped, but I finally realized why I was unsure of what was adjacent and what was opposite.

 

[Medgirl314]

Nope, I actually just realized I didn't figure it out yet. I was thinking of something else. Bummer.

 

[Medgirl314]

This would make the side with 3.0 m the hypotenuse. That doesn't look right, is that just because I am trying to trust the diagram?

 

[Konoha]

Aw! I was wondering what happened to you.
yes the 3.0 m hypotenuse is right.
Now, let's move back a little bit, the problem states that the rope is 3.0 m long and it's 1.1 meters above the ground at its lowest point. If we imagine it's hanging from the ceiling then we can say that the distance between the ground and ceiling is 4.1 m. right? In your diagram, mark that 4.1 m (just to visualise it).
Now using the diagram ( 3.0 m hypotenuse and cos34) what you get is the distance from the ceiling.
So it should be now pretty easy to find the height from the ground.
I'll be online for now. :)

 

[Medgirl314]

Thanks! Sorry, but the visualizing is making it a bit harder for me. To find the height above the ground(the answer) do I use 4.1cos(34) ?

 

[Konoha]

P.S. Just a quick reminder about adjacent and opposite. The side that together with hypotenuse is making the angle you are studying, is Adjacent. And the opposite is just like it's name, it's opposite that angle.

 

[Medgirl314]

Yes, I finally got that part last week, AFTER turning in a paper where I was going off the hypotenuse instead of my angle. XD So was I wrong about using cos?

 

[Konoha]

No, Take a look at this diagram, you are going to find x and then subtract it from 4.1 to find your final answer.
P.s. notice that the x is in the triangle you made, and Cos34 = adjacent / hypotenuse
and here the x is adjacent and hypotenuse is 3 m.

 

[Medgirl314]

So I was right about using cosine, but I also need to remember to subtract it from 4.1? I wasn't sure if you said "No, you aren right", or "No, you are wrong."

 

[Konoha]

Sorry, The "no" was the previous post.
You should use 3cos34, not 4.1cos34 (its should be always hypotenuse) which is 3m here.
and as you can see in the diagram this way you calculate x which is the distance from ceiling. but you want you find the distance from ground. and we know that the distance between ceiling and ground is 4.1.
so the final answer is: 4.1-x

 

[Medgirl314]

Ah, okay. Thanks! So about 1.61 meters?

 

[Konoha]

Yes! Correct :)

 

[Medgirl314]

That's the final answer? :-)

You should hang around. Smiley faces and politeness, not used to that here. XD