Question 149835
Let d = distance from the tower's base to the end of the string
d+2 = height of tower
.
d^2 + (d+2)^2 = 10^2
d^2 + (d^2+4d+4) = 100
2d^2 + 4d + 4 = 100
2d^2 + 4d - 96 = 0
d^2 + 2d - 48 = 0
factoring:
(d-6)(d+8) = 0
.
d = {-8, 6}
.
Since a negative answer doesn't make sense it must be:
d = 6 feet 
d+2= 8 feet (height of tower)