Question

What is the area of ΔABC given m∠B = 115°, a = 8 feet, and c = 13 feet?

Answer 1

Given:

`\begin{gathered} m\angle B=115^0 \\ a=8\text{feet} \\ c=13\text{feet} \end{gathered}`

Let us now sketch the triangle ABC

The formula to obtain the area(A) of the triangle is,

`A=(1)/(2)ac\sin B`

Therefore,

`\begin{gathered} A=(1)/(2)*8*13*\sin 115^0 \\ A=4*13*\sin 115^0=52\sin 115^0=47.128005feet^2\approx47.13feet^2(2\text{ decimal places)} \end{gathered}`

Hence, the area of the triangle ABC is

`47.13\text{feet}^2`

The correct option is Option 1.