https://file.aiquickdraw.com/mathbot/file/1728754632088pmvmkjl5.jpg

To solve for \( \tan(\theta) \) in the right-angled triangle shown, we use the formula:

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

In the given triangle:
- The opposite side to \( \theta \) is 10 cm.
- The adjacent side to \( \theta \) is 25 cm.

So, applying the formula:

\[
\tan(\theta) = \frac{10}{25} = 0.4
\]

Thus, \( \tan(\theta) = 0.4 \) in decimal form.

Would you like a more detailed explanation, or do you have any further questions?

Here are five related questions to deepen your understanding:
1. How would you calculate \( \sin(\theta) \) and \( \cos(\theta) \) for the same triangle?
2. What would happen to \( \tan(\theta) \) if the length of the adjacent side increased?
3. How is the value of \( \tan(\theta) \) affected in an isosceles right-angled triangle?
4. Can you find the angle \( \theta \) using the inverse tangent function?
5. How does the Pythagorean theorem relate to this problem?

**Tip**: Remember, \( \tan(\theta) \) gives you the ratio of the opposite side to the adjacent side, and it only works in right-angled triangles!

Write tan(θ) as a decimal for a right-angled triangle with opposite = 10 cm and adjacent = 25 cm.

Learn how to calculate the tangent (tan) of angle θ for a right-angled triangle where the opposite side is 10 cm and the adjacent side is 25 cm. This problem is suitable for students in Grades 8-10 and covers trigonometric ratios in right-angled triangles.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation