Find the area

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.

A = 50°, b = 30 ft, c = 14 ft


Correct result:

A =  160.87 ft²

Solution:

$$\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ a=\sqrt{30^2+14^2-2\cdot 30\cdot 14\cdot \cos 50^{\circ }}=23.581ft \\ s={\displaystyle \frac{1}{2}}(a+b+c)=33.7905ft \\ S=\sqrt{s(s-a)(s-b)(s-c)}=160.87{\text{ft}}^2 \end{gathered}$$

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