Question

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

$a=5,A=25°$

Short answer

Required values of the triangle are$B=65°,b=10.7,c=11.81$

Step-by-step solution

Step 1. Given information

$a=5,A=25°$

For the right triangle shown in figure , we have

$c^2=a^2+b^2,A+B=90°$

Step 2. Calculation

$$\begin{gathered} Weknow, \\ ForB, \\ \Rightarrow A+B=90° \\ \Rightarrow B=90°-A \\ =90°-25° \\ =65° \\ Forb, \\ \Rightarrow \tan \left(A\right)=\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$b$}\right. \\ \Rightarrow b=\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$\tan \left(A\right)$}\right. \\ =\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$\tan \left(25°\right)$}\right. \\ =\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$0.4663$}\right. \\ =10.7 \\ Forc, \\ \Rightarrow c^2=a^2+b^2 \\ =5^2+10.7^2 \\ =25+114.49 \\ =139.49 \\ \Rightarrow c=\sqrt{139.49}=11.81 \end{gathered}$$