The given triangle is shown:
Recall the formula for the Tangent Ratio in a right triangle:
[tex]\tan \theta=\frac{\text{opposite leg}}{adjacent\text{ leg}}[/tex]
Notice from the figure that the length of the leg opposite the angle is given as x and the length of the leg adjacent is 10.
Substitute these values into the tangent ratio with θ=27⁰:
[tex]\tan 27^{\circ}=\frac{x}{10}[/tex]
Solve the equation for x:
[tex]\begin{gathered} Cross\text{ Multiply:} \\ \Rightarrow x=10\tan 27^{\circ} \end{gathered}[/tex]
Evaluate the expression:
[tex]x\approx5.10\text{ units}[/tex]
The value of x is about 5.10 units.
