Question

Determine the area of a triangle with A=27.8 B = 107.3 c=4 Answer: B) 10 units^2

Answer 1

Correct question:

Determine the area of a triangle with A=27.8° B = 107.3° c=4

Answer:

Area of the triangle is 5.04 units²

Step-by-step explanation:

Given;

A = 27.8°

B = 107.3°

C = 180 - (27.8 + 107.3) = 44.9°

c = 4

Now, we determine the remaining two sides of the triangle using sine rule

$\frac{Sine \ A}{a} = \frac{Sine \ C}{c} \\\\a = \frac{Sine A*\ c}{Sine C} = \frac{Sine(27.8) \ *4}{Sine(44.9) } =2.64\\\\\frac{Sine \ B}{b} = \frac{Sine \ C}{c}\\\\b= \frac{Sine B*\ c}{Sine C} = \frac{Sine(107.3) \ *4}{Sine(44.9) } =5.41$

Apply Hero's formula;

$A = \sqrt{s(s-a)(s-b)(s-c)} \\\\s = \frac{a+b+c}{2} = \frac{2.64\ +\ 5.41\ +\ 4}{2} = 6.025\\\\A = \sqrt{6.025(6.025-2.64)(6.025-5.41)(6.025-4)} \\\\A = \sqrt{6.025(3.385)(0.615)(2.025)} \\\\A = \sqrt{25.3989} = 5.04 \ units^2$

Therefore, area of the triangle is 5.04 units²