Question

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

$a=6,B=40°;findb,c,andA$

Short answer

The respective values are

$$\begin{gathered} A=50° \\ b=7.15 \\ c=9.33 \end{gathered}$$

Step-by-step solution

Given information

$a=6,B=40°;findb,c,andA$

Calculation

$$\begin{gathered} SinceB=40°, \\ A+B=90° \\ \Rightarrow A=50° \\ Now, \\ \tan \left(40\right)=\frac{6}{b} \\ \sin \left(40\right)=\frac{6}{c} \\ Nowsolvingfora,c \\ b=\frac{6}{\tan \left(40\right)} \\ =7.15 \\ c=\frac{6}{\sin \left(40\right)} \\ =9.33 \end{gathered}$$