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ab = 5
bac = 90 degree
dac = 20 degree
ad= ?
ac = ?

To solve the problem, we need to find the lengths of \( AD \) and \( AC \) using the given information.

### Given:
1. \( AB = 5 \) units
2. \( \angle BAC = 90^\circ \) (Right angle)
3. \( \angle DAC = 20^\circ \)

### Find:
1. Length of \( AD \)
2. Length of \( AC \)

### Step-by-Step Solution:

#### Step 1: Use the Right Triangle \( \triangle ABC \)

Since \( \triangle ABC \) is a right triangle with \( \angle BAC = 90^\circ \), we can apply trigonometric ratios.

- \( \angle DAB = \angle DAC = 20^\circ \)
- \( \angle ABC = 90^\circ \)
  
Thus, in the right triangle \( \triangle ABC \):
- \( \tan(\angle BAC) = \frac{AB}{AC} \)

We know that:

\[
\tan(20^\circ) = \frac{AD}{AC}
\]

From this information, we can solve for \( AC \) and \( AD \). 


Learn how to find the lengths of AD and AC in a right triangle with AB = 5 units, angle BAC = 90 degrees, and angle DAC = 20 degrees using trigonometric ratios. This problem involves right triangle geometry and trigonometry, suitable for high school students.

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