Respuesta :

EXPLANATION

We can apply the Cosine Theorem in order to get the value of the Area as shown as follows:

[tex]c^2=a^2+b^2-2ab\cos C[/tex]

Substituting terms:

[tex]c^2=12^2+24^2-2\cdot12\cdot24\cdot\cos 26[/tex]

Computing the powers:

[tex]c^2=144+576-576\cdot\cos 26[/tex]

Computing the argument and adding numbers:

[tex]c^2=720-517.705[/tex]

Subtracting numbers:

[tex]c^2=202.295[/tex]

Applying the square root to both sides:

[tex]c=\sqrt[]{202.295}=14.22[/tex]

Now, the area of the triangle is given by the Heron's Formula:

[tex]\text{Semiparameter}=s=\frac{a+b+c}{2}=\frac{12+24+14.223}{2}=25.112[/tex][tex]\text{Area of triangle=}\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]

Substituting terms:

[tex]\text{Area of triangle=}\sqrt[]{25.112(25.112-12)(25.112-24)(25.112-14.223)}[/tex][tex]\text{Area of triangle=}\sqrt[]{25.112(25.112-12)(25.112-24)(25.112-14.223)}[/tex]

Multiplying and computing terms:

[tex]\text{Area of triangle=}63.125in^2[/tex]

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