Respuesta :

Check the picture below.

now we simply plug all those three sides in Heron's Area Formula.

[tex]\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=5.8\\ b=9.75\\ c=7.39\\ s=11.47 \end{cases} \\\\\\ A=\sqrt{11.47(11.47-5.81)(11.47-9.75)(11.47-7.39)} \\\\\\ A=\sqrt{11.47(5.66)(1.72)(4.08)}\implies A\approx \sqrt{455.5839955} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 21.3444~\hfill[/tex]

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SociometricStar

Answer:

area of triangle ABC is 21.39 square units.

C is the correct option.

Step-by-step explanation:

We know the formula for the area of the triangle ABC in terms of sine. The formulas are

[tex]A=\frac{1}{2}ab\sin C\\\\A=\frac{1}{2}ac\sin B\\\\A=\frac{1}{2}bc\sin A[/tex]

In the given triangle, we hae

b = 9.75

c = 7.39

A = 36.43°

Therefore, area of triangle ABC is given by

[tex]A=\frac{1}{2}bc\sin A\\\\\frac{1}{2}\cdot9.75\cdot7.39\sin36.43\\\\A=21.39[/tex]

Hence, area of triangle ABC is 21.39 square units.

C is the correct option.

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