Check the picture.
Let BC represent the wall, AC the ladder and AB the distance of the feet of the ladder to the wall.
ABC form a right triangle, with m(B)=90°, m(A)=60° and m(C)=30°.
AB is the side opposite the angle 30°, so the length of AB is half of the length of the hypotenuse AC.
Thus, let |AC|=2x, and |AB|=x.
By the Pythagorean theorem:
[tex] (2x)^{2}= x^{2} +30^{2} [/tex]
[tex] 4x^{2}= x^{2} +30^{2} [/tex]
[tex] 3x^{2}=30^{2}=900 [/tex]
[tex] x^{2}=300 [/tex]
thus [tex]x= 10\sqrt{3} [/tex]
the length of the ladder is [tex]2x= 20\sqrt{3}=34.64 [/tex] feet
Answer: [tex]20\sqrt{3}=34.64 [/tex] feet
