Question

Find the value of tan G rounded to the nearest hundredth, if necessary. The hypotenuse is 4 and the adjacent side is 3 and the opposite side is the square root of 7.

Answer 1

To find the value of \( \tan G \), we use the definition of tangent in a right triangle, which is given by the formula:

\[
\tan G = \frac{\text{opposite side}}{\text{adjacent side}}
\]

In this case, the opposite side is \( \sqrt{7} \) and the adjacent side is \( 3 \).

Now we can plug in the values to calculate \( \tan G \):

\[
\tan G = \frac{\sqrt{7}}{3}
\]

Next, we need to compute the value of \( \frac{\sqrt{7}}{3} \):

1. First, calculate \( \sqrt{7} \):
\[
\sqrt{7} \approx 2.6457513110645906
\]

2. Now, we divide this by \( 3 \):
\[
\frac{\sqrt{7}}{3} \approx \frac{2.6457513110645906}{3} \approx 0.881917
\]

Finally, rounding \( 0.881917 \) to the nearest hundredth gives us:

\[
\tan G \approx 0.88
\]

Thus, the value of \( \tan G \) rounded to the nearest hundredth is

\[
\boxed{0.88}
\]