Given, a right angled `Delta ABC`, whose base is 6 and perpendicular height is 8. Find the trigonometric ratios of sin A, cos A and tan A, respectively.

Options

A. `(4)/(5), (3)/(5), (4)/(3)`
B. `(2)/(5), (3)/(5), (4)/(5)`
C. `(4)/(5), (1)/(5), (2)/(3)`
D. None of these

Answer

To find the trigonometric ratios of sin A, cos A, and tan A for the right-angled triangle ABC with a base of 6 and a height of 8, we can follow these steps:

### Step 1: Identify the sides of the triangle
In triangle ABC:
- The base (adjacent side to angle A) = 6
- The height (opposite side to angle A) = 8

### Step 2: Calculate the hypotenuse using the Pythagorean theorem
The hypotenuse (AC) can be calculated using the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Substituting the values:
\[ AC^2 = 6^2 + 8^2 = 36 + 64 = 100 \]
Taking the square root:
\[ AC = \sqrt{100} = 10 \]

### Step 3: Calculate sin A
The sine of angle A is given by the ratio of the length of the opposite side to the hypotenuse:
\[ \sin A = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5} \]

### Step 4: Calculate cos A
The cosine of angle A is given by the ratio of the length of the adjacent side to the hypotenuse:
\[ \cos A = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{AB}{AC} = \frac{6}{10} = \frac{3}{5} \]

### Step 5: Calculate tan A
The tangent of angle A is given by the ratio of the length of the opposite side to the adjacent side:
\[ \tan A = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{BC}{AB} = \frac{8}{6} = \frac{4}{3} \]

### Final Results
Thus, the trigonometric ratios are:
- \(\sin A = \frac{4}{5}\)
- \(\cos A = \frac{3}{5}\)
- \(\tan A = \frac{4}{3}\)

---