SOLUTION: suppose you need to construct a right triangle in which the shortest side is eight feet less than the longest side and the third side is seven feet more than the shortest side.
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Question 205537: suppose you need to construct a right triangle in which the shortest side is eight feet less than the longest side and the third side is seven feet more than the shortest side.
draw a picture and label all the sides.
(i cant seem to figure out how to label all sides?)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
problem:
suppose you need to construct a right triangle in which the shortest side is eight feet less than the longest side and the third side is seven feet more than the shortest side.
draw a picture and label all the sides.
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your picture can be found at the following website:
http://theo.x10hosting.com/
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look for 205537 and click on it.
if it's not there, wait about 30 minutes and try again.
it will be there.
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points of triangle are ABC.
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line AC is called side b (opposite angle B)
line BC is called side a (opposite angle A)
line AB is called side c (opposite angle C)
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angle C is 90 degrees making it the right angle of the triangle
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c is the longest side of the triangle because it is the hypotenuse.
a is the shortest side of the triangle because we made it that way.
b is the third side of the triangle.
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problem states that the shortest side is 8 feet less than the longest side.
that means that a = c - 8
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the problem also states that the third side is 7 feet more than the shortest side.
that means that b = a + 7
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we let c = x because we don't know how long it is and we allow x to represent the length of it.
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if a = c - 8 and c = x then a = x - 8
if b = a + 7 and a = x - 8 then b = (x - 8) + 7 = x - 1
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now we have:
a = x-8
b = x-1
c = x
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you can solve for x by using the pythagorean formula.
the pythagorean formula states that:
where c is the hypotenuse of the triangle.
we constructed the triangle so that side c would be the hypotenuse so the picture and the formula should be synchronized.
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my answer is:
c = 13
b = 12
a = 5
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you can see that a is the shortest side and is 8 less than c which is the longest side.
you can see that b is the third side and is 7 more than a which is the shortest side.
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if you solve it you should get the same answer.
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