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Let's find the exact trigonometric values for angle \( B \) using the given triangle dimensions:

Given:
- \( a = 48 \) (opposite to angle \( A \))
- \( b = 55 \) (opposite to angle \( B \))
- \( c = 73 \) (hypotenuse)

The trigonometric functions for angle \( B \) are defined as follows:

1. **\(\sin(B)\)**: Ratio of the opposite side to the hypotenuse.
   \[
   \sin(B) = \frac{b}{c} = \frac{55}{73}
   \]

2. **\(\cos(B)\)**: Ratio of the adjacent side to the hypotenuse.
   \[
   \cos(B) = \frac{a}{c} = \frac{48}{73}
   \]

3. **\(\tan(B)\)**: Ratio of the opposite side to the adjacent side.
   \[
   \tan(B) = \frac{b}{a} = \frac{55}{48}
   \]

4. **\(\sec(B)\)**: Reciprocal of cosine.
   \[
   \sec(B) = \frac{1}{\cos(B)} = \frac{73}{48}
   \]

5. **\(\csc(B)\)**: Reciprocal of sine.
   \[
   \csc(B) = \frac{1}{\sin(B)} = \frac{73}{55}
   \]

6. **\(\cot(B)\)**: Reciprocal of tangent.
   \[
   \cot(B) = \frac{1}{\tan(B)} = \frac{48}{55}
   \]

### Summary of Values:
- \(\sin(B) = \frac{55}{73}\)
- \(\cos(B) = \frac{48}{73}\)
- \(\tan(B) = \frac{55}{48}\)
- \(\sec(B) = \frac{73}{48}\)
- \(\csc(B) = \frac{73}{55}\)
- \(\cot(B) = \frac{48}{55}\)

Would you like more details on any of these calculations or have any questions?

### Related Questions:
1. What are the exact values of trigonometric functions for angle \( A \)?
2. How would the values change if the sides were different?
3. What is the significance of reciprocal trigonometric functions?
4. How do you verify these values using the Pythagorean identity?
5. How are these trigonometric functions applied in real-life scenarios?

**Tip:** Always remember that the trigonometric functions depend on the specific angle and the corresponding sides of the triangle!

Suppose a = 48, b = 55, and c = 73. Find the exact values of trigonometric functions for angle B.

Learn how to find the exact trigonometric values for angle B in a right triangle with sides a = 48, b = 55, and c = 73. This problem covers sine, cosine, tangent, and their reciprocal functions, using fundamental trigonometric formulas. Suitable for high school students.

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