Question

20.Solve the triangle: b = 100, c = 100, y = 70". If it is not possible, say so.This triangle is not solvable.Q = 40", a = 68.4, B = 70'a= 70', a = 68.4, B = 40"Q = 40", a = 100, B=70"

Answer 1

Answer:

$\begin{gathered} \alpha=\text{ 40\degree} \\ \beta=\text{ 70\degree} \\ a=68.4 \end{gathered}$

Step-by-step explanation:

By the theorem of intern angles of a triangle, we know that the sum of all intern angles of a triangle must be 180°, therefore:

*There are two equal angles because there are two equal sides

$\begin{gathered} \alpha=180-70-70 \\ \alpha=\text{ 40\degree} \\ \beta=\text{ 70\degree} \end{gathered}$

Now, applying the law of sines, we can find side a. The law of sines is represented by the following equation:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}$

Hence, if b=100, alpha=40° and betha=70°, solve for a:

$\begin{gathered} \frac{a}{\sin (40)}=\frac{100}{\sin (70)} \\ a=\frac{100\cdot\sin (40)}{\sin (70)} \\ a=\text{ 68.4} \end{gathered}$