Question

Find the area of the triangle. Round to the nearest tenth. A=47 b=32 ft c=19 ft

Answer 1

First we can find the length of 'a' using law of cosines:

`\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ a^2=32^2+19^2-2\cdot32\cdot19\cdot\cos (47\degree) \\ a^2=1024+361-1216\cdot0.682 \\ a^2=1385-829.31 \\ a^2=555.69 \\ a=23.57 \end{gathered}`

Now we can calculate the area of the triangle using Heron's formula:

`Area=\sqrt[]{p(p-a)(p-b)(p-c)}`

Where p is the semiperimeter of the triangle. So we have that:

`\begin{gathered} p=(32+19+23.57)/(2) \\ p=37.285 \\ \text{Area}=\sqrt[]{37.285(13.715)\mleft(5.285\mright)\mleft(18.285\mright)} \\ \text{Area}=222.3 \end{gathered}`

So the area of the triangle is 222.3 ft².