Answer:
p = 32.32; A = 47.91
Step-by-step explanation:
1. Calculate ∠B
∠A + ∠B + ∠C = 180°
60° + ∠B + 45° = 180°
∠B + 105° = 180°
∠B = 75°
2. Find sides BC and AC
We can use the Law of Sines
[tex]\dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB}[/tex]
(i) Find BC
[tex]\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.8660}{BC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.8661}{0.7071} = 11.02[/tex]
(ii) Find AC
[tex]\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.9659}{AC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.9659}{0.7071} = 12.29[/tex]
3. Find the perimeter
p = AB + AC + BC = 9 + 12.29 + 11.02 = 32.32
4. Find the area of the triangle
A general formula for the area of a triangle is
A = ½ab sinC
If we use ∠A, the formula becomes
A = ½ × 9 × 12.29 × sin60° = 55.30 × 0.8660 = 47.91
