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

Answer

To solve the problem step by step, we will analyze the triangle ABC with the given information.

### Step 1: Understand the triangle configuration
We have a right triangle ABC where:
- Angle B = 90°
- Side AB = y units (opposite to angle C)
- Side BC = √3 units (adjacent to angle A)
- Side AC = 2 units (hypotenuse)

### Step 2: Identify the sides in relation to angle A
In triangle ABC:
- The side opposite angle A (which is angle X) is side BC = √3 units.
- The hypotenuse (the side opposite the right angle) is side AC = 2 units.

### Step 3: Write the sine ratio for angle A
The sine of angle A (which is X) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore:
\[ \sin A = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AC} \]

### Step 4: Substitute the known values
Now, substituting the known values into the sine ratio:
\[ \sin X = \frac{BC}{AC} = \frac{\sqrt{3}}{2} \]

### Step 5: Final answer
Thus, the value of \(\sin X\) is:
\[ \sin X = \frac{\sqrt{3}}{2} \]