Answer:
Option A is correct.
Step-by-step explanation:
Vertex of triangle are marked in attached pic.
So, we are given that ∠A = 95° , ∠B = 35° and c = 14 cm
We use law of sines.
which has following expression,
[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,C}[/tex]
∠A + ∠B + ∠C = 180° (Angle sum property of triangle)
95 + 35 + ∠C = 180
∠C = 180 - 130
∠C = 50°
Now using Law of sines,
[tex]\frac{b}{sin\,B}=\frac{c}{sin\,C}[/tex]
[tex]\frac{b}{sin\,35}=\frac{14}{sin\,50}[/tex]
[tex]\frac{b}{0.57}=\frac{14}{0.77}[/tex]
[tex]b=\frac{14}{0.77}\times0.57[/tex]
[tex]b=10.36[/tex]
[tex]b=10\:\:(approx)[/tex]
[tex]\frac{a}{sin\,A}=\frac{c}{sin\,C}[/tex]
[tex]\frac{a}{sin\,95}=\frac{14}{sin\,50}[/tex]
[tex]\frac{a}{0.99}=\frac{14}{0.77}[/tex]
[tex]a=\frac{14}{0.77}\times0.99[/tex]
[tex]a=18.11[/tex]
[tex]a=18\:\:(approx)[/tex]
Now using area of triangle by herons formula,
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
Semi perimeter, s = [tex]\frac{a+b+c}{2}=\frac{18+10+14}{2}=21[/tex]
So we have,
[tex]Area=\sqrt{21(21-18)(21-10)(21-14)}}[/tex]
[tex]Area=\sqrt{21(3)(11)(7)}}=3\times7\sqrt{11}=21\times3.3=69.6\:cm^2[/tex]
Since there is approximation in above calculated values, We select ans nearest to calculated one.
Therefore, Option A is correct.
