Answer:
p = 32.317
A = 47.911
Step-by-step explanation:
given ∠A = 60
∠C = 45
AB = 9
From sum of all angles in triangle is 180
∠A + ∠B + ∠C = 180
60 + ∠B + 45 = 180
∠B = 180 - 105 = 75
∠B = 75
from sine rule in ΔABC
AB / sin C = BC / sin A
=> 9 / sin 45 = BC / sin 60
=> 9 / 1/[tex]\sqrt{2}[/tex] = BC / [tex]\sqrt{3} / 2[/tex]
=> [tex]9\sqrt{2} = BC * 2 / \sqrt{3}[/tex]
BC = [tex]9\sqrt{2} * \sqrt{3} / 2\\[/tex]
BC = 11.023
length of AC is
AC / sin B = AB / sin C
AC / sin 75 = 9 / sin 45
AC = 9 / 1/[tex]\sqrt{2} * sin 75[/tex]
= [tex]9\sqrt{2} * sin 75\\12.294[/tex]
perimeter of ΔABC
AB + BC + CA
= 9 + 11.023 + 12.294
= 32.317
Area of ΔABC is
= 1/2 * AB * AC * sin A
= 1/2 * 9 * 12.294 * sin 60
= 1/2 * 9 * 12.294 * √3/2
= 47.911
