Question

Use the triangle shown on the right and the given information to solve the triangle Find a,c,B

Answer 1

Since we are dealing with a right triangle, we can use the trigonometric identities shown below

`\begin{gathered} cos\theta=(A)/(H),tan\theta=(O)/(A) \\ \theta\rightarrow\text{ interior angle} \\ O\rightarrow\text{ opposite side to}\theta \\ A\rightarrow\text{ adjacent side to}\theta \\ H\rightarrow\text{ hypotenuse} \end{gathered}`

Therefore, in our case,

`\begin{gathered} cosA=(b)/(c)\Rightarrow c=(b)/(cosA)=(2)/(cos(20\degree))\approx2.13 \\ and \\ tanA=(a)/(b) \\ \Rightarrow a=btanA=2*tan(20\degree)\approx0.73 \end{gathered}`

Finally, notice that angles A and B are complementary angles; thus

`\begin{gathered} A+B=90\degree \\ \Rightarrow B=70\degree \end{gathered}`

Thus, the rounded answers are a=0.73, c=2.13, B=70°