Question

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

Explanation:

Step1: Recall trigonometric identity

In a right - triangle, $\sin\theta=\cos(90^{\circ}-\theta)$. When $\sin\theta = \cos\theta$, then $\theta=45^{\circ}$ because $\sin45^{\circ}=\frac{\sqrt{2}}{2}$ and $\cos45^{\circ}=\frac{\sqrt{2}}{2}$.

Step2: Check each triangle

In the first triangle, angles are $50^{\circ},40^{\circ},90^{\circ}$. In the second triangle, angles are $45^{\circ},45^{\circ},90^{\circ}$. In the third triangle, angles are $68^{\circ},22^{\circ},90^{\circ}$. In the fourth triangle, angles are $60^{\circ},30^{\circ},90^{\circ}$. The second triangle has a $45^{\circ}$ angle.

Answer:

The second triangle.