在三角形ABC中,a加b等于12,A等于60度B等于45度则a等于?b等于?
问题描述：
在三角形ABC中,a加b等于12,A等于60度B等于45度则a等于?b等于?
答
根据三角法则,
(sin ∠A)/a = (sin ∠B)/b = (sin ∠C)/c
所以,
(sin ∠A)/a = (sin ∠B)/b
(sin 60°)/a = (sin 45°)b
(sin 60°)/(12 - b) = (sin 45°)/b
b(sin 60°) = (12 - b)(sin 45°)
(b√3)/2 = [(12 - b)√2]/2
b√3 = (12 - b)√2
b√3 = 12√2 - b√2
3b² = 288 - 2b²
5b² = 288
b² = 57.6
b = 7.59 ( 2 d.p.)