stick into it? Please explain in terms of the Pythagorean Theorem. Thanks again.
2006-11-08 13:33:02 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The theory is this..
The square of the length of the hypotenuse is the sum of the squares of the adjacent sides.
In this case you have two built in triangles you can solve... the front and the side of thebox. you need to solve one of these to find the hypotenuse from the top of the box to the bottom opposite corner... (the diagonal line from the top rear corner to the bottom front corner) this is the longest stick possible that you can fit in a box of these dimensions
so that being said.. the side of the box measures 3 x 5
pythagorean theorem states (a^2+b^2=c^2)
therefore 3^2+5^2=c^2 --> 9+25=c^2 so C=5.8 ( square root of 34)
next we solve the "compound" triangle. using the "C" value we calculated as one of the sides in the new triangle.
5.8^2 + 4^2 = C^2 --> 34+16= C^2 --> 50=C^2
C=7.07 (square root of 50)
So the answer is no only a stick 7.07 feet long will fit
2006-11-08 13:44:26 · answer #1 · answered by Jonny B 5 · 0⤊ 0⤋
A^2 + B^2 = C^2
A diagonal of the base of the box:
sqrt( (3 * 3) + (4 * 4) ) = 5
A diagonal for the whole box uses the base diagonal as one leg and the height as the other leg of a second Pythagoran equation:
sqrt( (5 * 5) + (5 * 5) ) =
sqrt(50)
8 * 8 = 64
64 < 50
8 foot stick cannot fit into the box unless you change the shape of the stick and\or box.
2006-11-08 13:43:34 · answer #2 · answered by warmspirited 3 · 0⤊ 0⤋
No by using fact the field is 3-D, you ought to locate the gap from one desirable corner to the backside opposite one, it somewhat is the optimal rapidly distance interior the field. once you draw a diagram with this distance you get a triangle, with the top of the field and diagonal of the oblong base by using fact the top and base of triangle. you're searching for the hypotenuse of this triangle. top of field = 5 ft Diagonal of base = 5 ft (Pythagorean theorem with 3 and four as different 2 sides for the oblong base) in case you employ the Pythagorean theorem returned with the two sides of five ft, the hypotenuse of the triangle is around 7.07 ft, it somewhat is smaller than 8. So a 8 foot stick won't slot interior the field.
2016-12-28 16:37:34 · answer #3 · answered by Anonymous · 0⤊ 0⤋
is 8^2<=3^2+4^2+5^2?
is 64<=3+16+25=50 Nope, won't fit
2006-11-08 13:36:57 · answer #4 · answered by yupchagee 7 · 0⤊ 0⤋
it should fit corner to corner
2006-11-08 13:36:49 · answer #5 · answered by Anonymous · 0⤊ 0⤋