Hello everyone. I have a very embarrassing question to ask because I should know how to figure this out for a number of reasons. I'm building a play set for my kids this summer and I need to calculate how much lumber I'm going to need and the dimensions. The support structure for the swings will be in the shape of a triangle. The height of the triangle will be 7' forming a 90 degree angle at the height. I don't know how to solve for the the sides so that I will know how long the lumber needs to be. To complicate things further, I will be burying the post 48" deep.
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Right Triangle question.
- Thread starter Johnscott
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HallsofIvy
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- Jan 27, 2012
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It appears that you have four right triangle, each with two legs of length 7 feet. (Since the angle at the top is 90 degrees and the situation is symmetric, the angle on each side is 45 degrees and the "height" and "base" are the same.) By the Pythagorean theorem, the hypotenuse (the length of the wooden beam) is \(\displaystyle \sqrt{7^2+ 7^2}= 7\sqrt{2}= 9.9\) feet- round that to 10 feet. The "48 inches" that will be underground is 4 feet, making as total of 14 feet. Note that this 4 feet underground will be the hypotenuse of a right triangle with legs of length \(\displaystyle \sqrt{4^2/2}= \sqrt{8}= 2\sqrt{2}= 2.8\) feet. That is how long and deep you will need to dig the trench.
It appears that you have four right triangle, each with two legs of length 7 feet. (Since the angle at the top is 90 degrees and the situation is symmetric, the angle on each side is 45 degrees and the "height" and "base" are the same.) By the Pythagorean theorem, the hypotenuse (the length of the wooden beam) is \(\displaystyle \sqrt{7^2+ 7^2}= 7\sqrt{2}= 9.9\) feet- round that to 10 feet. The "48 inches" that will be underground is 4 feet, making as total of 14 feet. Note that this 4 feet underground will be the hypotenuse of a right triangle with legs of length \(\displaystyle \sqrt{4^2/2}= \sqrt{8}= 2\sqrt{2}= 2.8\) feet. That is how long and deep you will need to dig the trench.
Thanks for the reply Ivy but I think I should have been more clear. I'm not really trying to solve for the hypotenuse. Actually the hypotenuse won't be made of wood at all. The hypotenuse will the ground itself. I'm trying to solve for the other two sides. The 4' is the depth of the trench not the amount of the beam that will be buried. The length of beam that will be buried is what I need to know so that I can figure out the overall length of those sides.
HallsofIvy
Elite Member
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- Jan 27, 2012
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You missed my point- I understand that the distance between "feet" is the hypotenuse of the triangle having the two supports a legs and right angle at the top. My point was that if you draw a line from that right angle to the ground, you have two (and two more at the other end of the swing) right triangles with right angle at the ground and the two supports of the swing as hypotenuse.Thanks for the reply Ivy but I think I should have been more clear. I'm not really trying to solve for the hypotenuse. Actually the hypotenuse won't be made of wood at all. The hypotenuse will the ground itself. I'm trying to solve for the other two sides. The 4' is the depth of the trench not the amount of the beam that will be buried. The length of beam that will be buried is what I need to know so that I can figure out the overall length of those sides.
You missed my point- I understand that the distance between "feet" is the hypotenuse of the triangle having the two supports a legs and right angle at the top. My point was that if you draw a line from that right angle to the ground, you have two (and two more at the other end of the swing) right triangles with right angle at the ground and the two supports of the swing as hypotenuse.
Ah. Now I get it, it actually makes sense. See I told you I needed help. I vaguely remember this from middle school. Thanks so much.