Question

the sides of which diagram are correctly labeled with respect to angle a?

Explanation:

Step1: Recall right - triangle side definitions

In a right - triangle with respect to an acute angle \(A\), the hypotenuse is the longest side opposite the right - angle, the opposite side is the side that does not form the angle \(A\) among the non - hypotenuse sides, and the adjacent side is the non - hypotenuse side that forms the angle \(A\).

Step2: Analyze each diagram

In the correct diagram, the hypotenuse should be the longest side (opposite the right - angle), the side opposite angle \(A\) should be the non - hypotenuse side not forming angle \(A\), and the adjacent side should be the non - hypotenuse side forming angle \(A\).

Answer:

The third diagram (from the left in the top row) is correctly labeled. In it, the side opposite angle \(A\) is labeled "Opposite", the side adjacent to angle \(A\) (the non - hypotenuse side forming angle \(A\)) is labeled "Adjacent", and the longest side (opposite the right - angle) is labeled "Hypotenuse".