Question

find fg.
write your answer as an integer or as a decimal rounded to the nearest tenth
fg =

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 21^{\circ}\), the opposite side is \(FG\) and the adjacent side is \(EG = 8\). So, \(\tan(21^{\circ})=\frac{FG}{8}\).

Step2: Solve for \(FG\)

Multiply both sides of the equation \(\tan(21^{\circ})=\frac{FG}{8}\) by \(8\). We get \(FG = 8\times\tan(21^{\circ})\).
Using a calculator, \(\tan(21^{\circ})\approx0.3839\). Then \(FG=8\times0.3839 = 3.0712\approx3.1\).

Answer:

\(3.1\)