https://file.aiquickdraw.com/mathbot/file/172591996907534wyenes.jpg

The image shows two mathematical problems:

1. **Conversion to Degrees and Minutes:**
   - "58.7° ="
   - This asks to convert 58.7 degrees into degrees and minutes.

2. **Trigonometric Expression:**
   - "2 tan 45° + sin 30°"
   - This asks to evaluate the expression without using a scientific calculator.

Let's solve them one by one:

### 1. Conversion of 58.7° to degrees and minutes:
The decimal part (0.7°) of 58.7° needs to be converted into minutes.

- \( 0.7 \times 60 = 42 \) minutes.

Thus, 58.7° is equivalent to **58° 42'**.

### 2. Simplifying \( 2 \tan 45° + \sin 30° \):
- \( \tan 45° = 1 \)
- \( \sin 30° = 0.5 \)

Now, substitute these values into the expression:
\[
2 \times 1 + 0.5 = 2 + 0.5 = 2.5
\]

Therefore, the value of \( 2 \tan 45° + \sin 30° \) is **2.5**.

Would you like more details on either problem or have any further questions?

Here are five related questions to expand on:
1. How do you convert degrees into radians?
2. What is the general formula for converting a decimal degree into minutes and seconds?
3. What is the value of \( \cos 60° \) and why?
4. How can you simplify expressions involving other trigonometric ratios, such as \( \cot \) and \( \csc \)?
5. What are some common angles with easily known sine, cosine, and tangent values?

**Tip**: For common trigonometric angles (like 30°, 45°, and 60°), memorizing their sine, cosine, and tangent values can help you solve problems faster without needing a calculator.

Convert 58.7° to degrees and minutes, and evaluate 2 tan 45° + sin 30° without using a scientific calculator.

Learn how to convert 58.7° into degrees and minutes, and evaluate the trigonometric expression 2 tan 45° + sin 30° step-by-step without a scientific calculator. This problem covers degree-minute conversion and basic trigonometric identities. Suitable for Grades 9-11 students.

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