https://file.aiquickdraw.com/mathbot/file/1729194914446b82etyo1.jpg

Let's solve the given expression:

\[
8 \sin(60^\circ) + 18 \tan(30^\circ)
\]

### Step 1: Recall trigonometric values
- \(\sin(60^\circ) = \frac{\sqrt{3}}{2}\)
- \(\tan(30^\circ) = \frac{1}{\sqrt{3}}\)

### Step 2: Substituting the values
\[
8 \times \frac{\sqrt{3}}{2} + 18 \times \frac{1}{\sqrt{3}}
\]

Simplify each term:
\[
8 \times \frac{\sqrt{3}}{2} = 4\sqrt{3}
\quad \text{and} \quad
18 \times \frac{1}{\sqrt{3}} = 6\sqrt{3}
\]

### Step 3: Combine like terms
\[
4\sqrt{3} + 6\sqrt{3} = 10\sqrt{3}
\]

### Final Answer:
\[
10\sqrt{3}
\]

Let me know if you'd like further clarifications!

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Here are **five related questions** to deepen your understanding:
1. What are the values of other common trigonometric angles like \(45^\circ\) and \(90^\circ\)?
2. How can you rationalize \(\frac{1}{\sqrt{3}}\) to avoid square roots in the denominator?
3. What is the significance of special triangles (30-60-90, 45-45-90) in trigonometry?
4. How would the answer change if the expression were \(8 \cos(60^\circ) + 18 \cot(30^\circ)\)?
5. What are some real-world applications where sine and tangent functions are used?

**Tip:** Memorizing the key trigonometric values for special angles can make solving problems much quicker!

Work out the value of 8 sin(60°) + 18 tan(30°). Give your answer in its simplest form.

Learn how to solve the trigonometric expression 8 sin(60°) + 18 tan(30°) using key trigonometric values for special angles like 60° and 30°. This problem covers essential concepts like simplifying trigonometric expressions and using trigonometric ratios. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Step 1: Recall trigonometric values

Step 2: Substituting the values

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