Question

What is the area of ΔABC given a = 12 inches, b = 24 inches, and m∠C = 26°? 63.125 in.2 93.156 in.2 109.808 in.2 129.426 in.2

Answer 1

EXPLANATION

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

$c^2=a^2+b^2-2ab\cos C$

Substituting terms:

$c^2=12^2+24^2-2\cdot12\cdot24\cdot\cos 26$

Computing the powers:

$c^2=144+576-576\cdot\cos 26$

Computing the argument and adding numbers:

$c^2=720-517.705$

Subtracting numbers:

$c^2=202.295$

Applying the square root to both sides:

$c=\sqrt[]{202.295}=14.22$

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

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

Substituting terms:

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

Multiplying and computing terms:

$\text{Area of triangle=}63.125in^2$