Given two sides of a right triangle, to find a missing angle, follow the steps below.
Step 01: Find an adequate trigonometric identity.
Since the two legs of the triangle are known, use the equation for a tangent:
[tex]\text{tan(}\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex]
Step 02: Substitute the values in the equation.
In this exercise,
8 is the opposite side;
5 is the adjacent side to θ.
Then,
[tex]\begin{gathered} \tan (\theta)=\frac{8}{5} \\ \tan (\theta)=1.6 \end{gathered}[/tex]
Step 03: Find θ.
Use tan⁻¹ to find θ.
[tex]\begin{gathered} \theta=\tan ^{-1}(1.6) \\ \theta=57.99\degree \end{gathered}[/tex]
Answer: θ = 57.99°.
