Question

If θ
= 44 °
, what is the length of side x? Round your answer to the nearest hundredth. (2 decimal places)
12
X

Answer 1

To find the length of side \( x \) given that one side measures \( 12 \) and the angle \( \theta \) is \( 44^\circ \), we need to know the context in which these measurements are provided.

Assuming you are dealing with a right triangle where:
- \( 12 \) is the length of the adjacent side to angle \( \theta \), and
- \( x \) is the opposite side,

You can use the tangent function, which is defined as:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Thus,

\[
\tan(44^\circ) = \frac{x}{12}
\]

To find \( x \), rearrange the equation:

\[
x = 12 \cdot \tan(44^\circ)
\]

Now, we can calculate this value. First, find \( \tan(44^\circ) \):

Using a calculator:

\[
\tan(44^\circ) \approx 0.9657
\]

Now plug this value into the equation:

\[
x = 12 \cdot 0.9657 \approx 11.5884
\]

Now round to the nearest hundredth:

\[
x \approx 11.59
\]

Thus, the length of side \( x \) is approximately \( \boxed{11.59} \).