Question

Find the value of tan G rounded to the nearest hundreth if necessary

Answer 1

The tangen of an angle in a triangle is given by:

$\tan \theta=\frac{\text{opp}}{\text{adj}}$

where opp and adj means the opposite and adjacent legs, respectively.

In this case we have that:

$\tan G=\frac{EF}{FG}$

then we need to find the length of leg EF. Using the pythagorean theorem we have:

$\begin{gathered} (\sqrt{24})^2=EF^2+3^2 \\ EF^2=(\sqrt{24})^2-3^2 \\ EF^2=15 \\ EF=\sqrt[]{15} \end{gathered}$

Now that we know the leg we need we have that:

$\begin{gathered} \tan G=\frac{\sqrt[]{15}}{3} \\ \tan G=1.29 \end{gathered}$

Therefore the tangent of G is 1.29