Question 98191
WHAT YOU HAVE IS A RIGHT TRIANGLE WITH AN HYPOTENUSE=50, A BASE =X & A HEIGHT=X+10.
USING THE PYTHAGOREON THEORUM WE GET {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
X^2+(X+10)^2=50^2
X^2+X^2+20X+100=2500
2X^2+20X+100-2500=0
2X^2+20X-2400=0
2(X^2+10X-1200)=0
2(X-30)(X+40)=0
X-30=0
X=30 ANSWER.
THEREFORE THE HEIGHT OF THE ANTENNA IS 30+10=40 FEET TALL.
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10A^2+AB-2B^2=0
(5A-2B)(2A+B)=0 ANSWER.