Sastādi pareizu malu attiecību, izmantojot vārdus: piekatete, pretkatete, hipotenūza! Taisnleņķa trijstūrī tgα=, kur α ir atbilstošais šaurais leņķis.

1. Break Down the Problem

To express the correct ratio of the sides in a right triangle using the terms provided (adjacent side, opposite side, hypotenuse), we need to relate these sides to the tangent function.

2. Relevant Concepts

In a right triangle:

• Opposite side: The side opposite the angle $\alpha$ (the side corresponding to the tangent function).
• Adjacent side: The side next to the angle $\alpha$.
• Hypotenuse: The longest side of the triangle, opposite the right angle.

The tangent function for an angle $\alpha$ is defined as: $\tan(\alpha) = \frac{\text{opposite}}{\text{adjacent}}$

3. Analysis and Detail

From the tangent definition, we know:

• $\text{opposite} = \text{pretkatete}$
• $\text{adjacent} = \text{piekatete}$

Thus, the expression becomes: $\tan(\alpha) = \frac{\text{pretkatete}}{\text{piekatete}}$

4. Verify and Summarize

This means that if we have the lengths of the opposite (pretkatete) and adjacent (piekatete) sides, we can find the tangent of the angle $\alpha$ using the ratio of these sides.

Final Answer

The correct ratio of the sides in a right triangle associated with the tangent function is: $\tan(\alpha) = \frac{\text{pretkatete}}{\text{piekatete}}$