To find the missing side length \( AB \) of a right triangle using the tangent ratio, you'll need to be given the lengths of the other side and the angle adjacent to the side you are trying to find.
The tangent of an angle in a right triangle is defined as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Where:
- \( \theta \) is the angle,
- "opposite" is the length of the side opposite the angle,
- "adjacent" is the length of the side adjacent to the angle.
If you have values for the angle and either the opposite or adjacent side, you can rearrange the formula to solve for the missing side.
For example, if we know:
- Angle \( \theta \)
- Length of adjacent side \( AC \)
- Length of opposite side \( BC \) (which is the side \( AB \) if \( AB \) is opposite \( \theta \))
Then, we can rearrange the tangent formula to get:
\[ AB = AC \cdot \tan(\theta) \]
If you provide specific values for \( \theta \) and either \( AC \) or \( BC \), I can help calculate \( AB \).
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