https://file.aiquickdraw.com/mathbot/file/1726172232496iyrptmxr.jpg

To find \( \tan(\theta) \), we can use the basic definition of the tangent function in a right triangle:

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

From the image:

- The side opposite to \( \theta \) is \( 10 \, \text{cm} \).
- The side adjacent to \( \theta \) is \( 45 \, \text{cm} \).

Thus, we can compute \( \tan(\theta) \) as:

\[
\tan(\theta) = \frac{10}{45} = \frac{2}{9} \approx 0.2222
\]

So, \( \tan(\theta) \approx 0.222 \).

Would you like more details or explanations?

Here are 5 related questions to further explore:

1. How would you calculate the angle \( \theta \) using \( \tan(\theta) \)?
2. What is the relationship between the sine and cosine of \( \theta \) and the sides of this triangle?
3. How can you calculate the hypotenuse using Pythagoras' theorem and verify the given length of 46.1 cm?
4. How would \( \tan(\theta) \) change if the adjacent side were shorter?
5. How is the tangent function used in trigonometric identities?

**Tip:** The tangent function can also be found using the sine and cosine of an angle: \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \).

Write tan(θ) as a decimal. The triangle has a height of 10 cm, a base of 45 cm, and a hypotenuse of 46.1 cm.

This problem helps calculate tan(θ) for a right triangle with a height of 10 cm, a base of 45 cm, and a hypotenuse of 46.1 cm. Learn how to apply the tangent function and solve for tan(θ) ≈ 0.2222 using basic trigonometric formulas. Suitable for high school students in grades 9-12.

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