Answer:
1. 3ft
2. 70.529°
Step-by-step explanation:
Question 1:
Calculated based on 2 given angles and 1 given side.
∠A = 180° - B - C = 0.5236 rad = π/6 = 30°
a = b·sin(A)/sin(B) = 3.4641 = 2[tex]\sqrt{3}[/tex]
c = b·sin(C)/sin(B) = 6.9282 = 4[tex]\sqrt{3}[/tex]
Area = [tex]\frac{ab·sin(C)}{2}[/tex] = 10.3923
Perimeter p = a + b + c = 16.3923
Semiperimeter s = [tex]\frac{a + b +c}{2}[/tex] = 8.19615
Height hα = [tex]\frac{2×Area}{a}[/tex] = 6
Height hb = [tex]\frac{2×Area}{b}[/tex] = 3.4641
Height hc = [tex]\frac{2×Area}{c}[/tex] = 3
Median ma = [tex]\sqrt{(a/2)2 + c2 - ac·cos(B)}[/tex] = 6.245
Median mb = [tex]\sqrt{(b/2)2 + a2 - ab·cos(C)}[/tex] = 4.58258
Median mc = [tex]\sqrt{(c/2)2 + b2 - bc·cos(A)}[/tex] = 3.4641
Inradius r = [tex]\frac{Area}{s}[/tex] = 1.26795
Circumradius R = [tex]\frac{a}{2sin(A)}[/tex] = 3.4641
Question 2:
Calculates b, ∠A, and ∠B based on given c, a, and ∠C.
∠A = arcsin([tex]\frac{a·sin(C)}{c}[/tex]) = 0.33984 rad = 19.471° = 19°28'16"
∠B = 180° - C - A = 1.23096 rad = 70.529° = 70°31'44"
b = [tex]\frac{c·sin(B)}{sin(C)\\}[/tex] = 11.31371 = 8√2
Area = [tex]\frac{ab·sin(C)}{2}[/tex] = 22.62742
Perimeter p = a + b + c = 27.31371
Semiperimeter s = [tex]\frac{a + b +c}{2}[/tex] = 13.65685
Height hα = [tex]\frac{2×Area}{a}[/tex] = 11.31371
Height hb = [tex]\frac{2×Area}{b}[/tex] = 4
Height hc = [tex]\frac{2×Area}{c}[/tex] = 3.77124
Median ma = [tex]\sqrt{(a/2)2 + c2 - ac·cos(B) }[/tex]= 11.48913
Median mb = [tex]\sqrt{(b/2)2 + a2 - ab·cos(C)}[/tex] = 6.9282
Median mc = [tex]\sqrt{√(c/2)2 + b2 - bc·cos(A)}[/tex] = 6
Inradius r = [tex]\frac{Area}{s}[/tex] = 1.65685
Circumradius R = [tex]\frac{a}{2sin(A)}[/tex] = 6
