Chapter 5 - Section 5.7 - Polynomial Equations and Their Applications - Exercise Set - Page 393: 82

12 ft

Apply the Pythagorean Theorem we have $c^2=a^2+b^2$ Thus, as per the given statement, we have $x^2+(x+4)^2=20^2$ or, $x^2+x^2+16+8x-400=0$ or, $2x^2+8x-384=0$ or, $x^2+4x-192=0$ Factorize as follows: $(x-12)(x+16)=0$ or, $x=-16,12$ Since, the height cannot be negative, thus, we have $x=12$ ft