It can be observed that AC and PR are the slides for younger and elder children respectively.
\\(\\begin{array}{l}{\ ext { In } \ riangle A B C,} \\\\ {\\frac{A B}{A C}=\\sin 30^{\\circ}} \\\\ {\\frac{1.5}{A C}=\\frac{1}{2}} \\\\ {A C=3 \\mathrm{m}}\\end{array}\\)
\\(\\begin{array}{l}{\ ext { In } \\Delta \\mathrm{PQR}_{,}} \\\\ {\\frac{\\mathrm{PQ}}{\\mathrm{PR}}=\\sin 60} \\\\ {\\frac{3}{\\mathrm{PR}}=\\frac{\\sqrt{3}}{2}} \\\\ {\\mathrm{PR}=\\frac{6}{\\sqrt{3}}=2 \\sqrt{3} \\mathrm{m}}\\end{array}\\)
Therefore, the length of these slides are 3 m and \\(2 \\sqrt{3} \\mathrm{m}\\).