https://file.aiquickdraw.com/mathbot/file/1729705065534q4jl0wxd.jpg

What is the value of tan(60°)?

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The image you've provided appears to show a right-angled triangle, and it seems you're asking for the value of \(\tan(60^\circ)\), possibly in the context of this triangle.

For any triangle, the tangent of an angle \(\theta\) is given by the ratio of the opposite side to the adjacent side:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

For \(\theta = 60^\circ\), in a standard 30-60-90 triangle, the value of \(\tan(60^\circ)\) is known to be:

\[
\tan(60^\circ) = \sqrt{3} \approx 1.732
\]

If you need more specific details related to this particular triangle in the image, such as calculating sides, feel free to let me know!

Would you like a detailed breakdown of this concept or do you have any additional questions?

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Here are 5 related questions to explore further:

1. How is the tangent function defined for different angles?
2. What are the properties of a 30-60-90 triangle?
3. How can you use trigonometric ratios to solve problems involving right triangles?
4. What is the relationship between the sine and cosine of an angle and its tangent?
5. How can the tangent of an angle be used in real-life applications like slope and height measurements?

**Tip:** Always remember that \(\tan(\theta)\) is undefined for angles where the adjacent side is zero, such as \(90^\circ\).

Explore the calculation of tan(60°) in a 30-60-90 right triangle. Learn how the tangent function is defined as the ratio of the opposite side to the adjacent side and how to use it in solving trigonometric problems. Suitable for students in Grades 9-12.

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