Question

If the angle is 73 degrees in a right triangle and the hypotenuse is 16, what is the adjacent? Answer with 4 decimal places

Answer 1

To find the length of the adjacent side in a right triangle, we can use the cosine function, which relates the adjacent side to the hypotenuse. The formula is:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Given that \(\theta = 73^\circ\) and the hypotenuse is 16, we can rearrange the formula to solve for the adjacent side:

\[
\text{adjacent} = \text{hypotenuse} \cdot \cos(\theta)
\]

Now, plug in the values:

\[
\text{adjacent} = 16 \cdot \cos(73^\circ)
\]

Calculating \(\cos(73^\circ)\):

\[
\cos(73^\circ) \approx 0.2924
\]

Now substituting this value:

\[
\text{adjacent} = 16 \cdot 0.2924 \approx 4.6784
\]

So, the length of the adjacent side is approximately:

\[
\text{adjacent} \approx 4.6784
\]

Thus, the final answer to four decimal places is:

\[
\boxed{4.6784}
\]