Answer:
Perimeter: 32.317
Area: 47.905
Step-by-step explanation:
Since there are 180 degrees in a triangle, mB=180-60-45=75 degrees. Since angle C is opposite of side AB, we can use the law of sines.
[tex]\dfrac{\sin{45^{\circ}}}{9} = \dfrac{\sin{75^{\circ}}}{AC} = \dfrac{\sin{60^{\circ}}}{BC} \\ \\ \therefore \\AC=\dfrac{9\cdot\sin{75^{\circ}}}{\sin{45^{\circ}}} \approx 12.294 \\\\\\BC=\dfrac{9\cdot\sin{60^{\circ}}}{\sin{45^{\circ}}} \approx 11.023[/tex]
Adding the side lengths together, we find that the perimeter is about 32.317. Now, we can use Heron's formula to find the area. Using s as the perimeter divided by 2, we can simply plug in the numbers:
[tex]s=32.317 \div 2=16.158\\\\A = \sqrt{s(s-AB)(s-BC)(s-AC)} = \sqrt{16.158(7.158)(5.135)(3.864)} \approx 47.905[/tex]
Answers are rounded to nearest 3rd decimal place.
