Răspuns:
Explicație pas cu pas:
7) a/sinA=b/sinB = c/sinC (t.sinsurilor)
sin75 = sin(30+45) = sin30cos45 +sin45cos30 =
1/2*√2/2 + √2/2*√3/2 = 1/4(√2 +√6)
<C = 180-75-30 = 45
a/sin75 =12/sin60 = c/sin45
a/sin75 =12/sin60
a/( 1/4(√2 +√6))=12/(√3/2)
4a/(√2 +√6) = 24/√3
4a*√3 = 24(√2 +√6)
a = 6(√2 +√6)/√3 = 6(√6 +√18)/3= 2(√6 +3√2)
12/sin60 = c/sin45
12/(√3/2) = c/(√2/2)
24/√3 = 2c/√2
c = 24√2/2√3 = 12√2/√3 = 12√6/3 = 4√6
Perim= 2(√6 +3√2) +12 + 4√6 =
6√6 +6√2 +12 = 6(√6 +√2 +6)
