Given : ` 4 cot A = 3 ` , find :
sinA

Answer

To solve the problem step by step, we start with the given equation and find the value of sin A.

### Step 1: Start with the given equation
We are given:
\[ 4 \cot A = 3 \]

### Step 2: Solve for cot A
To isolate cot A, divide both sides of the equation by 4:
\[ \cot A = \frac{3}{4} \]

### Step 3: Understand cotangent in terms of a right triangle
Recall that:
\[ \cot A = \frac{\text{base}}{\text{perpendicular}} \]
From our equation, we can assign:
- Base = 3
- Perpendicular = 4

### Step 4: Use the Pythagorean theorem to find the hypotenuse
We need to find the hypotenuse (h) of the right triangle using the Pythagorean theorem:
\[ h = \sqrt{(\text{perpendicular})^2 + (\text{base})^2} \]
Substituting the values:
\[ h = \sqrt{4^2 + 3^2} \]
\[ h = \sqrt{16 + 9} \]
\[ h = \sqrt{25} \]
\[ h = 5 \]

### Step 5: Find sin A
Now we can find sin A using the definition of sine:
\[ \sin A = \frac{\text{perpendicular}}{\text{hypotenuse}} \]
Substituting the values:
\[ \sin A = \frac{4}{5} \]

### Final Answer
Thus, the value of sin A is:
\[ \sin A = \frac{4}{5} \]

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