8. (w) ratios to find the lengths. .S) Find bº, x and z, each to two decimals. For x and z, use only trig 60 32°

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Find b, x, and z each to two decimals. Find x and z, using only trig ratios to find the lengths. 

### Trigonometry Problem Solving

**Problem Statement:**

Given a right triangle with one of the angles measuring 32 degrees.

1. Label the sides and angles as follows:
   - b: the length of the side adjacent to the 32-degree angle
   - x: the length of the side opposite to the 32-degree angle
   - z: the length of the hypotenuse
   - The remaining angle (that isn't 90 degrees) is labeled as 32 degrees.

2. Assign the side lengths:
   - The hypotenuse (z) forms the hypotenuse of the triangle.
   - The length of the adjacent side (b) lies next to the 32-degree angle.
   - The length of the opposite side (x) lies opposite to the 32-degree angle.
   
3. The remaining information provided is a right-angle denoted by a small square in the corner.

**Tasks:**

- Use trigonometric ratios (sine, cosine, and tangent) to find the following lengths each to two decimal places:
  - b: Adjacent to the 32-degree angle.
  - x: Opposite to the 32-degree angle.
  - z: The hypotenuse of the triangle.

**Trigonometric Formulas:**

To find the length of each side, we can use the following formulas:
1. \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
2. \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)
3. \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

Since angle \(\theta = 32^\circ\):

1. **To find the hypotenuse (z):**
   - Use either the sine or cosine function depending on which side length you have.
   
2. **To find the adjacent side (b):**
   - \( b = z \cdot \cos(32^\circ) \)

3. **To find the opposite side (x):**
   - \( x = z \cdot \sin(32^\circ) \)

Note: Typically, if no initial side length is given, often a length ratio or unit measure may be assumed to apply trigonometric rules. If additional information such as initial side lengths is available, apply
Transcribed Image Text:### Trigonometry Problem Solving **Problem Statement:** Given a right triangle with one of the angles measuring 32 degrees. 1. Label the sides and angles as follows: - b: the length of the side adjacent to the 32-degree angle - x: the length of the side opposite to the 32-degree angle - z: the length of the hypotenuse - The remaining angle (that isn't 90 degrees) is labeled as 32 degrees. 2. Assign the side lengths: - The hypotenuse (z) forms the hypotenuse of the triangle. - The length of the adjacent side (b) lies next to the 32-degree angle. - The length of the opposite side (x) lies opposite to the 32-degree angle. 3. The remaining information provided is a right-angle denoted by a small square in the corner. **Tasks:** - Use trigonometric ratios (sine, cosine, and tangent) to find the following lengths each to two decimal places: - b: Adjacent to the 32-degree angle. - x: Opposite to the 32-degree angle. - z: The hypotenuse of the triangle. **Trigonometric Formulas:** To find the length of each side, we can use the following formulas: 1. \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \) 2. \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \) 3. \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \) Since angle \(\theta = 32^\circ\): 1. **To find the hypotenuse (z):** - Use either the sine or cosine function depending on which side length you have. 2. **To find the adjacent side (b):** - \( b = z \cdot \cos(32^\circ) \) 3. **To find the opposite side (x):** - \( x = z \cdot \sin(32^\circ) \) Note: Typically, if no initial side length is given, often a length ratio or unit measure may be assumed to apply trigonometric rules. If additional information such as initial side lengths is available, apply
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