Question

identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.

Explanation:

Step1: Recall sine-cosine equality condition

For an acute angle $\theta$, $\sin\theta = \cos\theta$ when $\theta = 45^\circ$, since $\sin45^\circ = \cos45^\circ = \frac{\sqrt{2}}{2}$.

Step2: Match to the correct triangle

Look for the triangle with a $45^\circ$ acute angle. The second triangle (with $\angle A = 45^\circ$, $\angle B = 45^\circ$, right angle at $C$) has this angle.

Answer:

The second triangle (right triangle with $\angle A = 45^\circ$, $\angle B = 45^\circ$, right angle at $C$, and equal sides $AC$ and $BC$)