In `DeltaABC`, angle B is right angle, AB = 15 cm and BC = 8 cm. The value of sin A is :

Options

A. `15/17`
B. `8/17`
C. `15/8`
D. `8/15`

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:
- Angle B = 90°
- AB = 15 cm (this is one leg of the triangle)
- BC = 8 cm (this is the other leg of the triangle)

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

Substituting the known values:
\[ AC^2 = 15^2 + 8^2 \]
\[ AC^2 = 225 + 64 \]
\[ AC^2 = 289 \]

Now, take the square root to find AC:
\[ AC = \sqrt{289} = 17 \text{ cm} \]

### Step 3: Find sin A
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Here, for angle A:
- Opposite side (BC) = 8 cm
- Hypotenuse (AC) = 17 cm

Thus, we can write:
\[ \sin A = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AC} \]
\[ \sin A = \frac{8}{17} \]

### Final Answer
The value of sin A is:
\[ \sin A = \frac{8}{17} \]

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