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The problem you've shared involves solving a right triangle where one of the angles is 49°, and the adjacent side (labeled \( \sqrt{3} \, \text{ft} \)) is given. The task is to find the missing angle and sides (base and hypotenuse).

### Step-by-Step Solution:

#### 1. **Find the Missing Angle:**
- In a triangle, the sum of all angles is 180°. Since this is a right triangle, one angle is already 90°, and another is given as 49°.
  
  \[
  \text{Missing angle} = 90^\circ - 49^\circ = 41^\circ
  \]

So, the missing angle is **41°**, which seems to be correctly identified in your input.

#### 2. **Find the Base (Adjacent Side):**
- You can use trigonometric ratios to find the base (adjacent side).
- We know the adjacent side to the 49° angle is the given leg \( \sqrt{3} \, \text{ft} \), and we need to find the base (opposite to the 49° angle).

- The formula for the tangent of an angle is:

  \[
  \tan(49^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\text{base}}{\sqrt{3}}
  \]
  
  Solving for the base:

  \[
  \text{base} = \tan(49^\circ) \times \sqrt{3}
  \]
  
  \[
  \text{base} \approx 1.1503 \times 1.732 = 1.99 \, \text{ft}
  \]

The correct base length is approximately **1.99 ft**.

#### 3. **Find the Hypotenuse:**
- You can also use the sine or cosine function to find the hypotenuse.
- Using cosine for the given angle:

  \[
  \cos(49^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{\sqrt{3}}{\text{hypotenuse}}
  \]

  Solving for the hypotenuse:

  \[
  \text{hypotenuse} = \frac{\sqrt{3}}{\cos(49^\circ)}
  \]

  \[
  \text{hypotenuse} = \frac{1.732}{0.6561} \approx 2.64 \, \text{ft}
  \]

The hypotenuse is approximately **2.64 ft**.

### Final Answers:
- **Missing angle** = 41° (correct)
- **Base** = 1.99 ft (correction needed, not 1.50 ft)
- **Hypotenuse** = 2.64 ft (correction needed, not 2.30 ft)

Would you like further details on any step?

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Here are 5 related questions to practice:

1. How do you find the length of the opposite side using sine in a right triangle?
2. What is the relationship between the angles in any triangle?
3. How can you verify the accuracy of the base using the Pythagorean theorem?
4. How does changing the angle affect the length of the sides in a right triangle?
5. What would the base be if the given angle were 30° instead of 49°?

**Tip:** Always cross-check your results by using more than one trigonometric function to verify consistency in the answers.

Find the missing angle and sides of the given triangle. Round your answers to the nearest hundredth.

Solve for the missing angle, base, and hypotenuse of a right triangle. The problem involves trigonometric functions and requires knowledge of the tangent and cosine ratios, as well as the Pythagorean theorem. Suitable for students in Grades 9-10.

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