The image shows a right triangle with an angle θ. The side opposite θ is 3, adjacent is 4, and the hypotenuse is 5. We are asked to find the value of sin²θ + cos²θ.

This is a fundamental trigonometric identity. For any angle θ, the sum of the squares of sine and cosine is always 1. This is derived from the Pythagorean theorem applied to a unit circle or a right triangle.

Mathematically, this is expressed as: ${\sin \theta }^2+{\cos \theta }^2=1$

Therefore, regardless of the triangle's side lengths, the answer is always 1.

Final Answer: 1