If `sin theta = ( 8)/(17), ` then the value of `cos theta and tan theta ` is
(a) `(15)/(17), (8)/(15)`
(b) `(15)/(8) , (8)/(15)`
(c) `(15)/(17), (15)/(8)`
(d) None of these

Options

A. `(15)/(17), (8)/(15)`
B. `(15)/(8) , (8)/(15)`
C. `(15)/(17)`
D. None of these

Answer

To solve the problem, we start with the given information:

**Given:**
\[ \sin \theta = \frac{8}{17} \]

### Step 1: Create a Right-Angle Triangle
We can visualize this by creating a right-angle triangle where:
- The opposite side (perpendicular) to angle \( \theta \) is \( 8 \).
- The hypotenuse is \( 17 \).

### Step 2: Use Pythagorean Theorem to Find the Adjacent Side
According to the Pythagorean theorem:
\[ \text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2 \]

Substituting the known values:
\[ 17^2 = 8^2 + \text{Adjacent}^2 \]
\[ 289 = 64 + \text{Adjacent}^2 \]
\[ \text{Adjacent}^2 = 289 - 64 = 225 \]
\[ \text{Adjacent} = \sqrt{225} = 15 \]

### Step 3: Calculate \( \cos \theta \)
Using the definition of cosine:
\[ \cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{15}{17} \]

### Step 4: Calculate \( \tan \theta \)
Using the definition of tangent:
\[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{8}{15} \]

### Final Values
Thus, we have:
\[ \cos \theta = \frac{15}{17}, \quad \tan \theta = \frac{8}{15} \]

### Conclusion
The correct answer is:
\[ \text{(a) } \left( \frac{15}{17}, \frac{8}{15} \right) \]

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