Question

If the angle is 73 degrees in a right triangle and the hypotenuse is 16, what is the adjacent?

Answer 1

In a right triangle, you can find the length of the adjacent side using the cosine function. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Given:
- Angle \( \theta = 73^\circ \)
- Hypotenuse \( h = 16 \)

We can use the formula:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Rearranging this helps us find the length of the adjacent side:
\[
\text{adjacent} = \text{hypotenuse} \cdot \cos(\theta)
\]

Substituting the known values:
\[
\text{adjacent} = 16 \cdot \cos(73^\circ)
\]

Now, calculating \( \cos(73^\circ) \):
Using a calculator,
\[
\cos(73^\circ) \approx 0.2924
\]

Now multiply:
\[
\text{adjacent} \approx 16 \cdot 0.2924 \approx 4.6784
\]

So, the length of the adjacent side is approximately \( \boxed{4.68} \).