Question

What is the approximate area of the triangle below ?

Answer 1

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,

$\frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,C}$

∠A + ∠B + ∠C = 180°  (Angle sum property of triangle)

95 + 35 + ∠C = 180

∠C = 180 - 130

∠C = 50°

Now using Law of sines,

$\frac{b}{sin\,B}=\frac{c}{sin\,C}$

$\frac{b}{sin\,35}=\frac{14}{sin\,50}$

$\frac{b}{0.57}=\frac{14}{0.77}$

$b=\frac{14}{0.77}\times0.57$

$b=10.36$

$b=10\:\:(approx)$

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$\frac{a}{sin\,A}=\frac{c}{sin\,C}$

$\frac{a}{sin\,95}=\frac{14}{sin\,50}$

$\frac{a}{0.99}=\frac{14}{0.77}$

$a=\frac{14}{0.77}\times0.99$

$a=18.11$

$a=18\:\:(approx)$

Now using area of triangle by herons formula,

$Area=\sqrt{s(s-a)(s-b)(s-c)}}$

Semi perimeter, s = $\frac{a+b+c}{2}=\frac{18+10+14}{2}=21$

So we have,

$Area=\sqrt{21(21-18)(21-10)(21-14)}}$

$Area=\sqrt{21(3)(11)(7)}}=3\times7\sqrt{11}=21\times3.3=69.6\:cm^2$

Since there is approximation in above calculated values, We select ans nearest to calculated one.

Therefore, Option A is correct.

Answer 2

Answer:

72.8

Step-by-step explanation: