Question

What is the approximate area of the triangle below ?

Answer 1

72.8

Explanation:

Answer 2

Option A is correct.

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,

`(a)/(sin\,A)=(b)/(sin\,B)=(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,

`(b)/(sin\,B)=(c)/(sin\,C)`

`(b)/(sin\,35)=(14)/(sin\,50)`

`(b)/(0.57)=(14)/(0.77)`

`b=(14)/(0.77)*0.57`

`b=10.36`

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

`(a)/(sin\,A)=(c)/(sin\,C)`

`(a)/(sin\,95)=(14)/(sin\,50)`

`(a)/(0.99)=(14)/(0.77)`

`a=(14)/(0.77)*0.99`

`a=18.11`

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

Now using area of triangle by herons formula,

`Area=√(s(s-a)(s-b)(s-c))}`

Semi perimeter, s =
`(a+b+c)/(2)=(18+10+14)/(2)=21`

So we have,

`Area=√(21(21-18)(21-10)(21-14))}`

`Area=√(21(3)(11)(7))}=3*7√(11)=21*3.3=69.6\:cm^2`

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

Therefore, Option A is correct.