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

Explanation:

Step1: Recall trigonometric identity

We know that $\sin\theta=\cos(90^{\circ}-\theta)$. When $\sin\theta = \cos\theta$, then $\theta=90^{\circ}-\theta$.

Step2: Solve for the angle

Adding $\theta$ to both sides of $\theta = 90^{\circ}-\theta$, we get $2\theta=90^{\circ}$, so $\theta = 45^{\circ}$.

Step3: Identify the triangle

We look for the triangle with a $45^{\circ}$ acute - angle. The second triangle has two $45^{\circ}$ acute - angles.

Answer:

The second triangle (the one with two $45^{\circ}$ angles)