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

Step-by-step 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=(a+b+c)/(2)=(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`