Question

三角形ABC中。∠C=90°。若B=4根号5，C=12求a，∠A的正弦值，余弦值及三角形ABc面积

Answer 1

a=√(144 - 80) = 8
sina = a/c = 8/12 =2/3
cosa = b/c = 4√5/12 = √5/3
三角形ABC的面积 = ab/2 = 16√5

Answer 2

这是一直角三角形
c^2=a^2+b^2
c=12,b=4√5,a=8
cos∠A＝4√5/12=√5/3
sin∠A＝8/12=2/3
S△ABC＝1/2*4√5*8＝16√5

Answer 3

⊿ABC中,∠C=90º b=4√5 c=12
由勾股定理可知
a²+b²=c²
∴a=√(c²-b²)=√[12²-(4√5)²]=√(144-80)=√64=8
∴a=8
由三角函数定义
sinA=a/c=8/12=2/3
cosA=b/c=√5/3
S=(ab)/2=8×(4√5)÷2=16√5

Answer 4

∠C=90°，b=4√5，c=12
a = √(c^2-b^2) = √{12^2-(4√5)^2} = √(144-80) = 8
sinA = a/c = 8/12 = 2/3
cosA = b/c = 4√5/12 = √5/3
S = 1/2ab = 1/2*8*4√5 = 16√5