SOLUTION: i have a right triangle with a 90 degree angle and a hypotenuse of 18 i need to find the two short side lengths pleassse (:

Question 661169: i have a right triangle with a 90 degree angle and a hypotenuse of 18 i need to find the two short side lengths pleassse (:
Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

"I have a right triangle with a 90 angle..." What other kind of right triangle is there?

You have to provide some additional information. There are an infinite number of pairs of measures that satisfy

Another thing: Why "pleassse"? Is that more emphatic than "pleasse" or simply please? Why didn't you write "pleasssse" or "pleassssse"? Would that have been too 'over the top'?

John

My calculator said it, I believe it, that settles it

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you need to know the length of one of the sides.
otherwise, you will have 1 equation in 2 unknowns which can't be solved for a single value but can be solved for a multiple number of values if you assume a number for one for one of them.
example:
triangle is a right triangle with a hypotenuse of 18.
the pythatogean formula says that a^2 + b^2 = c^2 where a and b are legs and c is the hypotenuse.
square the 18 to get 324
your equation now becomes a^2 + b^2 = 324
you can solve for a in terms of b or you can solve for b in terms of a but you can't solve for a or b directly because you have 1 equation with 2 unknowns.

if you assume a value for a, then you can find a value for b.
if you assume a value for b, then you can find a value for a.

let's assume that a is equal to 8.
this means that a^2 = 64 and the equation becomes:
64 + b^2 = 324
subtract 64 from both sides of the equation to get b^2 = 324 - 64 which becomes b^2 = 260.
take the square root of both sides of that equation to get b = sqrt(260).

you have a = 8 and b = sqrt(260).
to find the hypotenuse use the pythagorean formula again to get:
a^2 + b^2 = c^2 which becomes:
8^ + sqrt(260)^2 = 18^2
simplify to get 64 + 260 = 324
combine like terms to get 324 = 324
the equation is true so a = 8 and b = sqrt(260) is a solution to the equation.

to get this solution, you had to assume a = 8.
if you are given the value of one of the legs and the hypotenuse, then you can solve for the other leg.

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