In `DeltaABC`, right angled at B, AB = 21 cm and BC = 20. The value of `sinA` is :

Options

A. `(21)/(29)`
B. `(20)/(21)`
C. `(20)/(29)`
D. `(21)/(20)`.

Answer

To find the value of \( \sin A \) in triangle \( ABC \) where \( \angle B \) is a right angle, we can follow these steps:

### Step 1: Identify the sides of the triangle
In triangle \( ABC \):
- \( AB = 21 \, \text{cm} \) (adjacent side to angle \( A \))
- \( BC = 20 \, \text{cm} \) (opposite side to angle \( A \))

### Step 2: Use the Pythagorean theorem to find the hypotenuse \( AC \)
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the values:
\[ AC^2 = 21^2 + 20^2 \]
Calculating the squares:
\[ AC^2 = 441 + 400 \]
\[ AC^2 = 841 \]
Now, taking the square root to find \( AC \):
\[ AC = \sqrt{841} = 29 \, \text{cm} \]

### Step 3: Calculate \( \sin A \)
The sine of angle \( A \) is defined as the ratio of the length of the side opposite to angle \( A \) to the length of the hypotenuse:
\[ \sin A = \frac{BC}{AC} \]
Substituting the known values:
\[ \sin A = \frac{20}{29} \]

### Final Answer
Thus, the value of \( \sin A \) is:
\[ \sin A = \frac{20}{29} \]

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