ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ︽ᠮᠣᠩᠭᠤᠯ ᠨᠤᠲᠤᠭ︾ ᠤᠷᠠᠨ ᠪᠢᠴᠢᠯᠭᠡ ᠪᠠᠶᠠᠨᠬᠦᠦ ᠪᠢᠴᠢᠪᠡᠢ .pdf ﹇ ᠳᠡᠯᠭᠡᠷᠡᠩᠭᠦᠢ ﹈

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ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ︽ᠨᠠᠭᠤᠨᠪᠢᠯᠢᠭ᠌ ᠣᠲᠠᠴᠢ ᠶᠢᠨ ᠵᠠᠭᠤᠨ ᠦᠰᠦᠭᠲᠦ ᠰᠢᠯᠦᠭ︾ ᠤᠷᠠᠨ ᠪᠢᠴᠢᠯᠭᠡ ᠪᠠᠶᠠᠨᠬᠦᠦ ᠪᠢᠴᠢᠪᠡᠢ .pdf ﹇ ᠳᠡᠯᠭᠡᠷᠡᠩᠭᠦᠢ ﹈

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠣᠷ ᠢ ᠶᠢ ᠰᠤᠳᠤᠭ ᠡᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪ ᠠᠢᠴ ᠠᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ︶ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠲᠤᠪ ᠃ ︵ ᠰᠡᠲᠤᠪ ᠪᠦ ᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ ︶ 1 ᠨᠢᠭᠡ ᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢ ᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷᠠᠭ ᠠᠨ ᠵᠢᠷᠤᠭ ᠨᠢ ᠵᠢᠷᠤ ᠭ 1 ᠮᠡᠳᠤ ᠂ ᠲᠡ ᠭᠡᠪᠠᠯ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢ ᠨ ᠪ ᠡᠶ ᠡ ᠨᠢ\s A ᠪᠦᠭᠡᠷᠡ ᠩᠬᠡᠢ ᠪᠠ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠤᠷᠢ ᠨ ᠶᠢ ᠰᠦᠳᠦᠭᠡ ᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄\s9 0 ᠮᠢ ᠨᠦ᠋ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬᠤᠪ ᠢ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠲᠤᠪ ᠃ ︵ ᠰᠡᠲᠤᠪ ᠪᠦ ᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ ︶ 1 ᠢᠵᠢ ᠯᠢ ᠨᠢ ᠭᠡᠨ ᠴᠠᠭ ᠮᠦ᠋ ᠴᠠ ᠢᠢᠨ ᠨᠠᠷ ᠠᠠ ᠤ ᠭᠡᠷᠡᠯ ᠲᠤᠤᠷ ᠠ ᠂ ᠪᠠᠲᠤ ᠢᠢᠨ ᠰᠡᠬ ᠦᠳᠡᠷ ᠨᠢ ᠪ ᠠᠭᠠᠳᠤᠷ ᠦᠨ ᠰᠡᠬᠦᠳᠡ ᠷ ᠡᠴᠠ ᠤᠷᠳᠤ ᠪᠣᠯ ᠂ ᠢ ᠵᠢᠯᠢ ᠨᠢᠭᠡᠨ ᠵᠠᠮ ᠦᠨ ᠳ᠋ ᠧᠩ ᠦ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠣᠷ ᠢᠨ ᠵᠢᠷᠭᠤᠳᠤ ᠭᠠᠷ ᠪᠥᠯᠥ ᠭ ᠦᠨ ᠨᠢᠭᠡ ᠴᠢ ᠶᠢ ᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ︶ ᠨᠢᠭᠡ᠄ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠲᠤᠪ ᠃\sᠰᠡᠳᠦᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠡᠢᠳᠡ 30 ᠬᠤᠪᠢ ） 1 ᠨᠢᠭᠡᠨ ᠦᠢ ᠯᠡᠳᠪᠦᠷᠢ ᠳ᠋ᠤ 10 0 ᠲ ᠣᠨ ᠲᠦ᠋ ᠭᠦᠬᠡᠢ ᠮᠠᠲ᠋ᠧᠷ ᠢᠶᠠᠯ ᠪᠠᠢᠨ ᠠ᠂ ᠡᠳᠦᠷ ᠪᠦᠷᠢ 𝒙 ᠲᠣᠨ ᠬᠡᠷᠡᠭᠯᠡᠪ ᠡᠯ Y ᠡᠳᠦᠷ ᠵᠠᠷᠤᠵ ᠤ ᠬᠦ ᠷᠤᠨ ᠠ᠂ ᠲᠡᠭᠡᠪ ᠡᠯ 𝑦

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠣᠷ ᠢᠨ ᠵᠢᠷᠭᠤᠳᠤ ᠭᠠᠷ ᠪᠥᠯᠥ ᠭ ᠦᠨ ᠨᠢᠭᠡ ᠴᠢ ᠶᠢ ᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲ ᠠ 90 ᠮᠢᠨᠦ᠋ ᠲ᠂ 12 0 ᠬ ᠤᠪᠢ᠃\sᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤ ᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ ᠰ ᠡᠳᠦᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠡᠢᠳᠡ 30 ᠬᠤᠪᠢ\s1 ᠴᠡᠭ A 1,\s,B （3, ）ᠨᠢ ᠹᠦᠩᠺᠼ Y ᠶ ᠢᠨ ᠵᠢᠷᠤᠮᠠᠭ ᠲᠡᠭᠡᠷ ᠠ ᠣᠷᠤᠰ ᠢᠨ ᠠ᠃ ᠲᠡᠭᠡᠪ ᠡᠯ , ᠶ ᠢᠨ ᠶᠡ ᠬᠡ ᠪ ᠠᠭ ᠠ ᠶᠢᠨ ᠬᠣᠯ ᠪᠤᠭᠳᠠᠯ ᠨᠢ\s A B\sC D ᠲᠤᠭᠳᠠ ᠭᠠᠬᠤ ᠠ ᠷᠭ ᠠ ᠦᠭᠡ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠤᠷᠢ ᠨ ᠳ ᠣᠯᠣᠳᠤᠭᠠᠷ ᠪᠥ ᠯᠥᠭ ᠦᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ︶ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠲᠤᠪ ᠃\sᠰ ᠡᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ\s1 ᠬᠠᠷᠢᠴᠠᠯ ᠲᠤ ᡂᠢ ᠨᠢ 1 50 00 0 ᠪᠤᠯᠬ ᠤ ᠭᠠ ᠵᠠᠷ ᠤ ᠨ ᠵᠢᠷ ᠤᠭ ᠲᠡᠭᠡᠷ ᠠ ᠠ ᠂ ᠡ ᠬᠤᠶ ᠠᠷ ᠭᠠᠵᠠᠷ ᠤᠨ ᠬᠤᠭᠤᠷ ᠤᠨᠳᠤᠬ ᠢ ᠵᠠ ᠢ ᠨᠢ 25 CM ᠂ ᠲᠡ ᠭᠡᠪᠡᠯ ᠠ᠂ ᠡ ᠬᠤ ᠶᠠᠷ ᠭᠠᠵᠠ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠤᠷᠢ ᠨ ᠳᠣ ᠯᠣᠳᠤᠭᠠᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪᠠᠢ ᠴᠠᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵ 09 ᠡᠲᠢᠠ ᠨ ᠨᠦ᠋ᠨᠢᠮ 02 9 ᠢᠪᠤᠬ ︶ ᠨᠲᠭᠡ ᠰᠪᠩᠭᠪᠬ ᠤ ᠰᠡ ᠢᠪᠪ ᠃ ᠰᠡᠢᠪ ᠪ ᠪᠦᠷᠢ 4 ᠢ ᠪᠤᠬ ᠨᠦ᠋ᠨᠢᠮ 28 ᠢᠪ ᠤᠬ\s1 ᠳᠪᠪᠷ ᠦ᠋ᠬᠢ ᠤᠯᠦ᠋ᠨ ᠦᠨᠴᠦᠭᠢᠦ ᠡ ᠴᠮ ᠯᠦ᠋ᠤᠢᠦ᠋ ᠢ ᠢᠦ᠋ᠷ ᠲᠯᠴᠦ᠋ᠨ ᠲᠠ ᠰᠢᠦ᠋ᠢ ᠪᠤᠯ ᠬᠤ ᠨᠢ\s A ᠢᠪᠶ ᠦ᠋ᠷ ᠳᠡ ᠭᠰᠢ ᠦᠨᠴᠦᠭᠢᠦ B ᠢᠪᠶ ᠦ᠋ᠷ ᠷᠪᠮᠪ C ᠢᠪᠶ ᠦ᠋ᠷ ᠳᠡ ᠭᠰᠢ ᠲᠠᠷᠤ

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠣᠷ ᠢᠨ ᠨᠠᠢ ᠮᠠᠳᠤ ᠭᠠᠷ ᠪᠥᠯᠥ ᠭ ᠦᠨ ᠨᠢᠭᠡ ᠴᠢ ᠶᠢ ᠨ ᠪᠠᠢᠴᠠ ᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ 90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰ ᠡᠲᠤᠪ᠃ ᠰᠡ ᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ 1 ᠬᠡᠷᠪᠡ ᠥᠨᠴ ᠥᠭ 𝛼 ᠨᠢ ᠬᠤᠷᠴᠠ ᠥᠨ ᠴᠥᠭ ᠮᠥ ᠷᠳᠡᠭᠡ ᠨ𝑠𝑖𝑛𝛼\s45 ᠪᠣᠯ᠂ 𝑡𝑎𝑛𝛼\s︵ ︶ A 925 B 35 C 34 D 43 2 RT ∆AB C ᠳᠦ᠂ ∠C\s9

ᠲᠣᠪᠴᠢᠯᠠᠯ᠄ ᠬᠣᠷ ᠢᠨ ᠨᠠᠢ ᠮᠠᠳᠤ ᠭᠠᠷ ᠪᠥᠯᠥ ᠭ ᠦᠨ ᠨᠢᠭᠡ ᠴᠢ ᠶᠢ ᠨ ᠪᠠᠢᠴᠠ ᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ 90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ\sᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰ ᠡᠲᠤᠪ᠃ ᠰ ᠡᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ 1 ᠦᠭ᠍ ᠭᠦᠭ᠍ᠳ᠋ᠡᠭ᠍ ᠰᠡᠨ ᠨᠢ RT ∆A BC ᠳ᠋ᠥ ᠂ ∠C\s90 , AC\s6 , BC\s8 ᠲᠡᠭᠡᠪ ᠡᠯ SINA ᠵᠢᠨ ᠬᠡᠮᠵᠢ ᠭ᠍ᠳ᠋ᠡᠯ ᠨᠢ\s A 35 B 34 C