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The triangle in the image appears to be a right-angled triangle with one side labeled as 6 cm. There are two angles marked as 40° and an unknown angle (ψ).

Given the triangle is a right triangle and one angle is marked as 40°, the other non-right angle (ψ) can be found using the fact that the sum of angles in a triangle is always 180°:

\[
\psi = 90^\circ - 40^\circ = 50^\circ
\]

Now, we can solve for the other sides of the triangle using trigonometric functions. Since we know the hypotenuse (6 cm) and the angles, we can use the sine and cosine functions.

1. To find the adjacent side (let's call it \( a \)):
   \[
   \cos(40^\circ) = \frac{a}{6} \quad \Rightarrow \quad a = 6 \cdot \cos(40^\circ)
   \]

2. To find the opposite side (let's call it \( b \)):
   \[
   \sin(40^\circ) = \frac{b}{6} \quad \Rightarrow \quad b = 6 \cdot \sin(40^\circ)
   \]

Would you like me to calculate these values and provide further details, or explain any specific steps?

Here are some related questions:
1. What is the significance of the sum of angles in a triangle?
2. How do trigonometric functions relate to the sides of a right triangle?
3. What are the primary trigonometric identities for solving right triangles?
4. Can you solve for the area of this triangle given one side and two angles?
5. How would you apply the Pythagorean theorem here?

**Tip**: Always verify the sum of the angles in a triangle to ensure correct measurements.

Find the angles and sides of a right-angled triangle where one side is 6 cm and an angle is 40°.

Learn how to solve a right-angled triangle with one side of 6 cm and a 40° angle. This problem covers the sum of angles in a triangle and basic trigonometric functions like sine and cosine to find unknown sides and angles.

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