Question

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

$b=4,B=10°;finda,c,andA$

Short answer

The respective values are

$$\begin{gathered} A=80° \\ a=0.35 \\ c=2.03 \end{gathered}$$

Step-by-step solution

Given information

$b=4,B=10°;finda,c,andA$

Calculation

$$\begin{gathered} SinceB=10°, \\ A+B=90° \\ \Rightarrow A=80° \\ Now, \\ \tan \left(10\right)=\frac{a}{2} \\ \cos \left(10\right)=\frac{2}{c} \\ Nowsolvingfora,c \\ a=2\tan \left(10\right) \\ =0.35 \\ c=\frac{2}{\cos \left(10\right)} \\ =2.03 \end{gathered}$$