Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

Find The Area Of The Triangle Round To The Nearest Tenth A47 B32 Ft C19 Ft class=

Sagot :

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

[tex]\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}[/tex]

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

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

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

[tex]\begin{gathered} p=\frac{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}[/tex]

So the area of the triangle is 222.3 ft².

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.