If `sqrt(3)=1*732`, find (correct to two decimal places) the value of each of the following :
(i) `sin60^(@)" (ii) "2/(tan30^(@))`

Answer

To solve the problem step by step, we will find the values of \( \sin 60^\circ \) and \( \frac{2}{\tan 30^\circ} \) using the given value of \( \sqrt{3} = 1.732 \).

### Step 1: Calculate \( \sin 60^\circ \)

We know that:
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]
Now, substituting the given value of \( \sqrt{3} \):
\[ \sin 60^\circ = \frac{1.732}{2} \]

### Step 2: Perform the division

Calculating \( \frac{1.732}{2} \):
\[ \sin 60^\circ = 0.866 \]

### Step 3: Round to two decimal places

Rounding \( 0.866 \) to two decimal places gives:
\[ \sin 60^\circ \approx 0.87 \]

### Step 4: Calculate \( \frac{2}{\tan 30^\circ} \)

We know that:
\[ \tan 30^\circ = \frac{1}{\sqrt{3}} \]
Thus, we can express \( \frac{2}{\tan 30^\circ} \) as:
\[ \frac{2}{\tan 30^\circ} = 2 \cdot \sqrt{3} \]

### Step 5: Substitute the value of \( \sqrt{3} \)

Now substituting the value of \( \sqrt{3} \):
\[ \frac{2}{\tan 30^\circ} = 2 \cdot 1.732 \]

### Step 6: Perform the multiplication

Calculating \( 2 \cdot 1.732 \):
\[ \frac{2}{\tan 30^\circ} = 3.464 \]

### Step 7: Round to two decimal places

Rounding \( 3.464 \) to two decimal places gives:
\[ \frac{2}{\tan 30^\circ} \approx 3.46 \]

### Final Answers
- \( \sin 60^\circ \approx 0.87 \)
- \( \frac{2}{\tan 30^\circ} \approx 3.46 \)