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The task is asking for calculations related to two triangles that are similar (trijstūri ir līdzīgi).

1. The sides of the first triangle are 18 cm and 23 cm, with the angle between them being 40°.
2. For the second triangle, we know that its corresponding side lengths are 3.7 times longer than those of the first triangle.
3. The angle between the corresponding sides of the second triangle is also 40°.

We are asked to:
- Calculate the sides of the second triangle.
- Determine why these triangles are similar (which characteristic makes them similar).

### Solution:

#### Step 1: Calculate the sides of the second triangle
Since the sides of the second triangle are 3.7 times the sides of the first triangle, the corresponding sides of the second triangle will be:

- First side: \( 18 \times 3.7 = 66.6 \, \text{cm} \)
- Second side: \( 23 \times 3.7 = 85.1 \, \text{cm} \)

#### Step 2: Similarity criteria
The two triangles are similar because they have equal angles (40°) and the sides adjacent to these angles are proportional by the factor 3.7. This matches the **Side-Angle-Side (SAS) similarity criterion** for triangles.

Do you need further details on any step, or have any questions?

### 5 Related Questions:
1. How can we use trigonometry to find the third side of the first triangle?
2. What are the other similarity criteria for triangles?
3. How do we calculate the area ratio between two similar triangles?
4. Can we find the height of both triangles given their angles and side lengths?
5. How does knowing only one angle help in identifying similar triangles?

**Tip:** When triangles are similar, all their corresponding angles are equal, and their corresponding sides are in proportion.

Pirmā trijstūra malas ir 18 cm un 23 cm un leņķis starp tām ir 40°. Aprēķini otra trijstūra malas, ja zināms, ka tās ir 3.7 reizes garākas nekā pirmā trijstūra atbilstošās malas un leņķis starp šīm malām ir 40°. Nosaki, pēc kuras pazīmes abi trijstūri ir līdzīgi!

Learn how to calculate the sides of a triangle similar to another triangle with sides 18 cm and 23 cm and a 40° angle. The sides of the second triangle are 3.7 times longer, and we use the SAS Similarity Theorem to solve this geometry problem.

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