Answer:
a = 6.65
Area = 15.84
Step-by-step explanation:
By cosine rule in the given triangle,
BC² = AC² + AB² - 2(AC)(AB)cos(C)
a² = 5² + 9²- 2(5)(7)cos(28°)
a² = 25 + 81 - 61.81
a = [tex]\sqrt{44.19}[/tex]
a = 6.65
Area of a triangle with given three sides = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Here, s = Average of lengths of all sides
a, b and c are the measures of the respective sides of the triangle.
s = [tex]\frac{6.65+7+5}{2}[/tex]
s = 9.325
a = 6.65, b = 5 and c = 7
Now substitute these values in the formula to get the area,
Area = [tex]\sqrt{9.325(9.325-6.65)(9.325-5)(9.325-7)}[/tex]
= [tex]\sqrt{9.325\times 2.675\times 4.325\times 2.325}[/tex]
= [tex]\sqrt{250.8313}[/tex]
= 15.838
= 15.84
