In a `Delta ABC, angle A=90^(@), angle B=30^(@)` find the ratio of sides .

Answer

To find the ratio of the sides of triangle ABC where angle A = 90°, angle B = 30°, and angle C = 60°, we can follow these steps:

### Step 1: Identify the angles
In triangle ABC, we know:
- Angle A = 90°
- Angle B = 30°
- Angle C = 180° - (90° + 30°) = 60°

### Step 2: Use the properties of a 30-60-90 triangle
In a 30-60-90 triangle, the sides are in a specific ratio:
- The side opposite the 30° angle (let's call it AC) is \( x \).
- The side opposite the 60° angle (let's call it BC) is \( x\sqrt{3} \).
- The hypotenuse (AB) is \( 2x \).

### Step 3: Assign lengths to the sides
Let:
- AC = \( x \) (opposite angle B)
- BC = \( x\sqrt{3} \) (opposite angle C)
- AB = \( 2x \) (hypotenuse)

### Step 4: Write the ratio of the sides
The ratio of the sides AC : AB : BC can be expressed as:
- AC : AB : BC = \( x : 2x : x\sqrt{3} \)

### Step 5: Simplify the ratio
To simplify the ratio, we can factor out \( x \):
- AC : AB : BC = \( 1 : 2 : \sqrt{3} \)

### Final Answer
The ratio of the sides of triangle ABC is:
**1 : 2 : √3**

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