SOLUTION: I am building a garden box in an Isosceles triangle shape. The legs are 8 ft long, I don't know how to find the base length. can you please help. thank you.

Question 674365: I am building a garden box in an Isosceles triangle shape.
The legs are 8 ft long, I don't know how to find the base length.
can you please help.
thank you.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you can't find the base length unless you know the vertex angle.
that's the angle between the 2 equal sides.
the 2 equal sides are 8 feet long each.
the base will be any lengthy depending on the angle between the legs.
it will range from 0 to 16
it can't be equal to 0 because then your 2 legs will have collapsed against each other and there is no space left for the garden.
it can't be 180 degrees because the legs will have collapsed against the base and you will not have any space for the garden.
the angle has to be somewhere between 0 and 180 degrees but not equal to 0 or 180 degrees.
assuming an angle of 90 degrees, then your isosceles triangle will have 2 legs of 8 feet each and a base of with a length of square root of (128)
this is because by making the vertex angle 90 degrees, you created a right triangle with legs of 8 feet each and a hypotenuse as the base which means the pythagorean triangle formula can be used which is:
a^2 + b^2 = c^2
one of the legs if a and one of the legs is b and c is the base / hypotenuse of the isosceles triangle.
you get 8^2 + 8^2 = c^2 which results in 64 + 64 = c^2 which results in 128 = c^2 which results in c = square root of 128.
that's the length of the base, assuming the vertex angle is 90 degrees.
that length is equal to 11.3237085 in decimal format.
remember now, the vertex angle is the angle between the equal legs of the isosceles triangle.
change the angle, and the length of the base changes.

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