Question

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

$b=4,A=10°;finda,c,andB$

Short answer

The respective values are

$$\begin{gathered} B=80° \\ a=0.71 \\ c=4.06 \end{gathered}$$

Step-by-step solution

Given information

$b=4,A=10°;finda,c,andB$

Calculation

$$\begin{gathered} SinceA=10°, \\ A+B=90° \\ \Rightarrow B=80° \\ Now, \\ \tan \left(10\right)=\frac{a}{4} \\ \cos \left(10\right)=\frac{4}{c} \\ Nowsolvingfora,c \\ a=4\tan \left(10\right) \\ =0.71 \\ c=\frac{4}{\cos \left(10\right)} \\ =4.06 \end{gathered}$$