Question

A tree is supported by HELP! a wire anchored in the ground 9 feet from its base. the wire is 1 foot longer than the height that it reacheson the tree. find the length of the wire.
note:use Pythagorean theorem

Answer 1

A^2+b^2=c^2
a=length of tree
b=length of ground
C= length of wire
a=?
b= 9
C=a+1
plug in
a^2+9^2=(a+1)^2
simplify
a^2+81=a^2+2a+1
subtract -a^2 from both sides
subtract 1 from both sides
80=2a
divide both sides by 2
a=40
C=40+1
C=41

Answer 2

For a right triangle with legs legnth a and b and hyptonuse c
a^2+b^2=c^2
9 feet from base, that's one leg
wire is hypotnuse, it's 1 more than height on tree
c=b+1

so
9^2+b^2=(b+1)^2
81+b^2=b^2+2b+1
minus b^2+1 from both sides
80=2b
divide both sides by 2
40=b
c=b+1
c=40+1
c=41
legnth of wire is 41ft