Question

Use the right triangle shown below. Then, using the given information, solve the triangle.

$b=5,B=20°;finda,c,andA$

Short answer

The respective values are

$$\begin{gathered} A=70° \\ a=0.73 \\ c=2.13 \end{gathered}$$

Step-by-step solution

Given information

$b=5,B=20°;finda,c,andA$

Calculation

$$\begin{gathered} SinceB=20°, \\ A+B=90° \\ \Rightarrow A=70° \\ Now, \\ \tan \left(20\right)=\frac{a}{2} \\ \cos \left(20\right)=\frac{2}{c} \\ Nowsolvingfora,c \\ a=2\tan \left(20\right) \\ =0.73 \\ c=\frac{2}{\cos \left(20\right)} \\ =2.13 \end{gathered}$$