\\(1 \\lt a \\lt 2\\) \u3068\u3059\u308b. \\(3\\) \u8fba\u306e\u9577\u3055\u304c \\(\\sqrt{3} , a , b\\) \u3067\u3042\u308b\u92ed\u89d2\u4e09\u89d2\u5f62\u306e\u5916\u63a5\u5186\u306e\u534a\u5f84\u304c \\(1\\) \u3067\u3042\u308b\u3068\u3059\u308b. \u3053\u306e\u3068\u304d \\(a\\) \u3092\u7528\u3044\u3066 \\(b\\) \u3092\u8868\u305b.<\/p>\r\n
\u9577\u3055 \\(a , b , \\sqrt{3}\\) \u306e\u5404\u8fba\u306e\u5bfe\u89d2\u3092 \\(A , B , C\\) \u3068\u304a\u304f.
\r\n\u6b63\u5f26\u5b9a\u7406\u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{a}{\\sin A} = \\dfrac{b}{\\sin B} & = \\dfrac{\\sqrt{3}}{\\sin C} = 2 \\\\\r\n\\text{\u2234} \\quad \\sin A = \\dfrac{a}{2} , \\ \\sin B & = \\dfrac{b}{2} , \\ \\sin C = \\dfrac{\\sqrt{3}}{2} \\quad ... [1]\r\n\\end{align}\\]\r\n\\(C\\) \u306f\u92ed\u89d2\u306a\u306e\u3067\r\n\\[\r\nC = 60^{\\circ}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(B = 120^{\\circ} - A\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\sin B & = \\sin \\left( 120^{\\circ} - A \\right) \\\\\r\n& = \\dfrac{\\sqrt{3}}{2} \\cos A + \\dfrac{1}{2} \\sin A \\quad ... [2]\r\n\\end{align}\\]\r\n\\(A\\) \u306f\u92ed\u89d2\u306a\u306e\u3067, [1] \u3088\u308a\r\n\\[\\begin{align}\r\n\\cos A & = \\sqrt{1 -\\sin^2 A} = \\sqrt{1 -\\left( \\dfrac{a}{2} \\right)^2} \\\\\r\n& = \\dfrac{\\sqrt{4-a^2}}{2}\r\n\\end{align}\\]\r\n\u3053\u308c\u3068 [1] \u3092 [2] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\n\\dfrac{b}{2} & = \\dfrac{\\sqrt{3}}{2} \\cdot \\dfrac{\\sqrt{4-a^2}}{2} + \\dfrac{1}{2} \\cdot \\dfrac{a}{2} \\\\\r\n\\text{\u2234} \\quad b & = \\underline{\\dfrac{a +\\sqrt{3 \\left( 4-a^2 \\right)}}{2}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(1 \\lt a \\lt 2\\) \u3068\u3059\u308b. \\(3\\) \u8fba\u306e\u9577\u3055\u304c \\(\\sqrt{3} , a , b\\) \u3067\u3042\u308b\u92ed\u89d2\u4e09\u89d2\u5f62\u306e\u5916\u63a5\u5186\u306e\u534a\u5f84\u304c \\(1\\) \u3067\u3042\u308b\u3068\u3059\u308b. \u3053\u306e\u3068\u304d \\(a\\) \u3092\u7528\u3044\u3066 \\(b\\) \u3092 … \u7d9a\u304d\u3092\u8aad\u3080