Question

Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) A = 81°, b = 76, c = 39

Answer 1

First, let's find the measure of the third side, using the law of cosine:

`\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos(A)\\ \\ a^2=76^2+39^2-2\cdot76\cdot39\cdot\cos81°\\ \\ a^2=5776+1521-927.34\\ \\ a^2=6.369.66\\ \\ a=79.81 \end{gathered}`

Now, let's use Heron's formula to calculate the area:

`\begin{gathered} p=(a+b+c)/(2)=97.405\\ \\ A=√(p(p-a)(p-b)(p-c))\\ \\ A=1463.75 \end{gathered}`