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To find the length of \( AD \) in the right triangle \( \triangle ABC \) shown, where \( \angle B = 49^\circ \), \( \angle A = 23.2^\circ \), and \( BC = 16 \), we can use trigonometric ratios.

Given:
- \( \angle B = 49^\circ \)
- \( BC = 16 \) (hypotenuse in \( \triangle ABC \))

1. Since \( AD \) is adjacent to \( \angle B \), we use the cosine function:
   \[
   \cos(49^\circ) = \frac{AD}{BC}
   \]

2. Rearrange to solve for \( AD \):
   \[
   AD = BC \cdot \cos(49^\circ)
   \]
   \[
   AD = 16 \cdot \cos(49^\circ)
   \]

3. Calculate \( AD \):
   \[
   AD \approx 16 \cdot 0.6561 = 10.4976
   \]

So, \( AD \approx 10.5 \) units, rounded to the nearest tenth.

Would you like more detailed calculations or have any questions?

### Related Questions
1. How do you find the length of \( AB \) in the triangle?
2. What is the sine of \( \angle A \) in this triangle?
3. How would you calculate the area of \( \triangle ABC \)?
4. How does the Pythagorean theorem verify \( AD \) if we know \( AB \) and \( BC \)?
5. What trigonometric function relates \( AB \) and \( \angle B \)?

### Tip
In a right triangle, the cosine of an angle gives the ratio of the adjacent side to the hypotenuse, useful for calculating side lengths.

Learn how to find the length of AD in a right triangle with given angles and hypotenuse. This solution uses trigonometric ratios, specifically the cosine function, to calculate side lengths in right triangles. Ideal for high school students studying trigonometry.

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