Measurements of a triangle

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 answer:

S =  160.87 ft²

Step-by-step explanation:

$$\begin{gathered} A=50{}^{\circ } \\ b=30\text{ft} \\ c=14\text{ft} \\ {a}^2=b^2+c^2-2bc\cos A \\ a=\sqrt{b^2+c^2-2\cdot b\cdot c\cdot \cos A}=\sqrt{b^2+c^2-2\cdot b\cdot c\cdot \cos 50°}=\sqrt{30^2+14^2-2\cdot 30\cdot 14\cdot \cos 50°}=\sqrt{30^2+14^2-2\cdot 30\cdot 14\cdot 0.642788}=23.58089\text{ft} \\ s=\frac{a+b+c}{2}=\frac{23.5809+30+14}{2}\doteq 33.7904\text{ft} \\ S=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}=\sqrt{33.7904\cdot (33.7904-23.5809)\cdot (33.7904-30)\cdot (33.7904-14)}=160.87{\text{ft}}^2 \end{gathered}$$

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