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

Use The Triangle Shown On The Right And The Given Information To Solve The Triangle Find AcB class=

Sagot :

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

[tex]\begin{gathered} cos\theta=\frac{A}{H},tan\theta=\frac{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}[/tex]

Therefore, in our case,

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

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

[tex]\begin{gathered} A+B=90\degree \\ \Rightarrow B=70\degree \end{gathered}[/tex]

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