In `DeltaABC`, angle B is right angle, AB = 20 cm and BC = 21 cm. The value of sin A is :

Options

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

Answer

To find the value of sin A in triangle ABC where angle B is a right angle, AB = 20 cm, and BC = 21 cm, we can follow these steps:

### Step 1: Identify the sides of the triangle
In triangle ABC:
- Angle B is the right angle (90 degrees).
- AB is opposite to angle C (20 cm).
- BC is opposite to angle A (21 cm).

### Step 2: Use the Pythagorean theorem to find AC
According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

Substituting the given values:
\[ AC^2 = 20^2 + 21^2 \]
\[ AC^2 = 400 + 441 \]
\[ AC^2 = 841 \]
Taking the square root:
\[ AC = \sqrt{841} = 29 \, \text{cm} \]

### Step 3: Find sin A
The sine of angle A can be calculated using the formula:
\[ \sin A = \frac{\text{Opposite side to angle A}}{\text{Hypotenuse}} \]

In this case:
- The opposite side to angle A is BC (21 cm).
- The hypotenuse is AC (29 cm).

So,
\[ \sin A = \frac{BC}{AC} = \frac{21}{29} \]

### Final Answer
Thus, the value of sin A is:
\[ \sin A = \frac{21}{29} \]

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