Question

find the value of tan X rounded to the nearet hundredth, if necessary. the hypotenuse is 13 the opposite side is 12

Answer 1

To find the value of \( \tan X \), we use the definition of the tangent function in a right triangle:

\[
\tan X = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case, we know the length of the opposite side is 12. We need to find the length of the adjacent side using the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

where \( c \) is the hypotenuse, \( a \) is the opposite side, and \( b \) is the adjacent side. Here:

- \( c = 13 \)
- \( a = 12 \)

Substituting the values we have:

\[
13^2 = 12^2 + b^2
\]

Calculating the squares:

\[
169 = 144 + b^2
\]

Now, isolate \( b^2 \):

\[
b^2 = 169 - 144 = 25
\]

Taking the square root gives us the length of the adjacent side:

\[
b = \sqrt{25} = 5
\]

Now we can calculate \( \tan X \):

\[
\tan X = \frac{\text{opposite}}{\text{adjacent}} = \frac{12}{5}
\]

Calculating the value:

\[
\tan X = 2.4
\]

Rounded to the nearest hundredth, the value of \( \tan X \) is:

\[
\boxed{2.40}
\]