Question

If possible, find the area of the triangle defined by the following: a = 7, b = 4, y = 43°9.5 square units19.3 square units14 square units16.8 square units

Answer 1

`\begin{gathered} \frac{\text{ A }}{\sin\text{ A}}\text{ = }\frac{B}{\sin \text{ B}} \\ \frac{70}{\sin\text{ A}}\text{ = }\frac{100}{\sin \text{ 35}} \\ \sin \text{ A = }(70\sin 35)/(100) \\ \sin \text{ A = 40.15/ 100} \\ \sin \text{ A = 0.40} \\ \text{ A = 23.7\degree} \end{gathered}`

So C = 180 - 23.7 - 35

= 121.3°

`\begin{gathered} \text{ }\frac{C\text{ }}{\sin\text{ C}}\text{ = }\frac{B}{\sin \text{ B}} \\ \frac{C}{\sin\text{ 121.3}}\text{ = }\frac{100}{\sin \text{ 35}} \\ \text{ C = }\frac{100\sin \text{ 121.3}}{\sin \text{ 35}} \\ C\text{ = }(85.44)/(0.57) \\ C\text{ = 150 mi} \end{gathered}`