Question

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

$a=7,B=50°;findb,c,andA$

$a=7,B=50°;findb,c,andA$

Short answer

The respective values are

$$\begin{gathered} A=40° \\ b=5.87 \\ c=9.14 \end{gathered}$$

Step-by-step solution

Given information

$a=7,B=50°;findb,c,andA$

Calculation

$$\begin{gathered} SinceB=50°, \\ A+B=90° \\ \Rightarrow A=40° \\ Now, \\ \tan \left(50\right)=\frac{7}{b} \\ \sin \left(50\right)=\frac{7}{c} \\ Nowsolvingfora,c \\ b=\frac{7}{\tan \left(50\right)} \\ =5.87 \\ c=\frac{7}{\sin \left(50\right)} \\ =9.14 \end{gathered}$$