Question

By using the Right angled triangle and the information given below, solve the triangle.

$a=6,A=40°$

Short answer

Required values of the triangle are$b=7.2,c=9.37,B=50°$.

Step-by-step solution

Step 1. Given information

$a=6,A=40°$

For the right triangle shown in figure , we have

$c^2=a^2+b^2,A+B=90°$

Step 2. Calculation

$$\begin{gathered} Weknow, \\ ForB, \\ \Rightarrow A+B=90° \\ \Rightarrow B=90°-A \\ =90°-40° \\ =50° \\ Forb, \\ \Rightarrow \tan \left(A\right)=\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$b$}\right. \\ \Rightarrow b=\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$\tan \left(A\right)$}\right. \\ =\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$\tan \left(40°\right)$}\right. \\ =\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$0.839$}\right. \\ =7.2 \\ \Rightarrow c^2=a^2+b^2 \\ =6^2+7.2^2 \\ =36+51.84 \\ =87.84 \\ \Rightarrow c=\sqrt{87.84}=9.37 \end{gathered}$$