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The image provided involves a problem that relates to right triangles and trigonometric functions. Let's break down the problem:

### Given:
- A right triangle where one leg is \( a = 5 \) units and the other leg is \( b = 4 \) units.

### Task 1:
- The problem asks to calculate the length of the hypotenuse \( c \) using the Pythagorean theorem.

The Pythagorean theorem states:
\[
c = \sqrt{a^2 + b^2}
\]

### Task 2:
- The problem asks to calculate the sine, cosine, and tangent of the angle \( \theta \) where \( a \) is the opposite side and \( b \) is the adjacent side to \( \theta \).

#### 1. **Hypotenuse Calculation:**
\[
c = \sqrt{5^2 + 4^2} = \sqrt{25 + 16} = \sqrt{41} \approx 6.4
\]

#### 2. **Trigonometric Functions:**
Given:
- Opposite \( = a = 5 \)
- Adjacent \( = b = 4 \)
- Hypotenuse \( = c \approx 6.4 \)

**Sine \( \sin(\theta) \)**:
\[
\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{5}{6.4} \approx 0.78125
\]

**Cosine \( \cos(\theta) \)**:
\[
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{4}{6.4} \approx 0.625
\]

**Tangent \( \tan(\theta) \)**:
\[
\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{5}{4} = 1.25
\]

### Summary:
1. **Length of Hypotenuse \( c \)**: \( \approx 6.4 \)
2. **Sine \( \sin(\theta) \)**: \( \approx 0.78125 \)
3. **Cosine \( \cos(\theta) \)**: \( \approx 0.625 \)
4. **Tangent \( \tan(\theta) \)**: \( 1.25 \)

Would you like more details or have any questions?

### Relative Questions:
1. How would the trigonometric functions change if one of the legs of the triangle was doubled?
2. What is the value of \( \theta \) in degrees given the trigonometric ratios?
3. How does the Pythagorean theorem apply to non-right triangles?
4. What are the sine, cosine, and tangent of the complementary angle of \( \theta \)?
5. What is the relationship between the sine and cosine of \( \theta \) and \( 90^\circ - \theta \)?

### Tip:
Always remember that the sine, cosine, and tangent functions are directly tied to the angle's position in the right triangle relative to the sides.

Determine the hypotenuse of a right triangle with sides a = 5 and b = 4 using the Pythagorean theorem. Then calculate the sine, cosine, and tangent of the corresponding angle.

Learn how to determine the hypotenuse of a right triangle with sides 5 and 4 using the Pythagorean theorem. Discover how to find the sine, cosine, and tangent of the angle in the triangle with step-by-step calculations. Suitable for students in Grades 8-10.

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