In `DeltaABC, angleB=90^@), AB=y" units", BC=sqrt(3) " units"`, AC = 2 units and angle `A=x^(@)`, find :
`tanx^(@)`

Answer

To solve the problem, we will analyze the triangle ABC with the given information and find the value of \( \tan x^\circ \).

### Step-by-Step Solution:

1. **Identify the Triangle Configuration**:
- We have a right triangle \( \Delta ABC \) where \( \angle B = 90^\circ \).
- The sides are given as follows: \( AB = y \) units, \( BC = \sqrt{3} \) units, and \( AC = 2 \) units.

2. **Label the Triangle**:
- Let \( A \) be at the top, \( B \) at the right angle, and \( C \) at the bottom left.
- Thus, \( AB \) is the opposite side to angle \( A \), \( BC \) is the adjacent side to angle \( A \), and \( AC \) is the hypotenuse.

3. **Use the Pythagorean Theorem**:
- According to the Pythagorean theorem, in a right triangle:
\[ AC^2 = AB^2 + BC^2 \]
- Substituting the known values:
\[ 2^2 = y^2 + (\sqrt{3})^2 \]
\[ 4 = y^2 + 3 \]
- Solving for \( y^2 \):
\[ y^2 = 4 - 3 = 1 \implies y = 1 \]

4. **Find \( \tan x^\circ \)**:
- The tangent of angle \( A \) (which is \( x^\circ \)) is given by:
\[ \tan x^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AB} = \frac{\sqrt{3}}{1} = \sqrt{3} \]

5. **Conclusion**:
- Therefore, the value of \( \tan x^\circ \) is:
\[ \tan x^\circ = \sqrt{3} \]