Let the length of the ladder be \\\\(=15\\\\)m(hypotenuse)The angle between the ladder and the wall \\\\(\\angle{BCA}={60}^{\\circ}\\\\)Angle between ladder and the ground \\\\(\\angle{CAB} ={90}^{\\circ}-{60}^{\\circ}={30}^{\\circ}\\\\)Height of the wall \\\\(= BC\\\\)\\\\(\\sin{{30}^{\\circ}}=\\dfrac{BC}{15}\\\\)\\\\(\\Rightarrow \\dfrac{1}{2}=\\dfrac{BC}{15}\\\\)\\\\(\\Rightarrow BC=\\dfrac{15}{2}=7.5\\\\)m