Question

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

$b=4,c=6$

Short answer

Required values of the triangle are$a=4.47,A=48.17°,B=41.83°$

Step-by-step solution

. Given information

$b=a,c=6$

For the right triangle shown in figure , we have

$c^2=a^2+b^2,A+B=90°$

Step 2. Calculation

$$\begin{gathered} Weknow, \\ Forc, \\ \Rightarrow c^2=a^2+b^2 \\ \Rightarrow a^2=c^2-b^2 \\ =6^2-4^2 \\ =36-16 \\ =20 \\ \Rightarrow a=\sqrt{20}=4.47 \\ ForA, \\ \Rightarrow \tan \left(A\right)=\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$b$}\right. \\ =\raisebox{1ex}{$4.47$}\!\left/ \!\raisebox{-1ex}{$4$}\right. \\ =1.1175 \\ \Rightarrow A={\tan }^{-1}(1.1175)=48.17° \\ ForB, \\ \Rightarrow A+B=90° \\ \Rightarrow B=90°-A=90°-48.17°=41.83° \end{gathered}$$