Question

025 geometry b wwva
trigonometric ratios
identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.

Explanation:

Step1: Recall trigonometric ratio identities

For an acute - angle $\theta$ in a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$. If $\sin\theta=\cos\theta$, then the opposite side and the adjacent side to the angle $\theta$ must be equal.

Step2: Analyze the right - triangles

In a right - isosceles triangle (a triangle with two equal sides), the two acute angles are $45^{\circ}$. In a $45 - 45-90$ triangle, if we consider one of the $45^{\circ}$ angles, the opposite side and the adjacent side to that $45^{\circ}$ angle are equal. So, $\sin45^{\circ}=\cos45^{\circ}=\frac{\sqrt{2}}{2}$.

Answer:

The triangle with two $45^{\circ}$ angles (the first triangle in the image).