Question

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

$c=9,B=20°$

Short answer

Required values of the triangle are$A=70°,a=8.45,b=3.09$

Step-by-step solution

Step 1. Given information

$c=9,B=20°$

For the right triangle shown in figure , we have

$c^2=a^2+b^2,A+B=90°$

Step 2. Calculation

$$\begin{gathered} Weknow, \\ ForA, \\ \Rightarrow A+B=90° \\ \Rightarrow A=90°-B \\ =90°-20° \\ =70° \\ Fora, \\ \Rightarrow \sin \left(A\right)=\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$c$}\right. \\ \Rightarrow a=\sin \left(A\right)\times c \\ =\sin (70°)\times 9 \\ =0.9396\times 9 \\ =8.45 \\ Forb, \\ \Rightarrow c^2=a^2+b^2 \\ \Rightarrow b^2=c^2-a^2 \\ =9^2-8.{45}^2 \\ =81-71.4025 \\ =9.5975 \\ \Rightarrow b=\sqrt{9.5975}=3.09 \end{gathered}$$