Question

what type of triangles do you use the trig ratios with? any type right triangle acute triangle obtuse triangle

Explanation:

Step1: Recall trigonometric ratios definition

Trigonometric ratios (sine, cosine, tangent) are defined based on the sides of a right - triangle. For a right - triangle with an acute angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Analyze other triangle types

• Acute triangle: If we want to use trigonometric ratios in an acute non - right triangle, we usually divide it into two right - triangles (by drawing an altitude) and then apply trigonometric ratios.
• Obtuse triangle: Similarly, for an obtuse non - right triangle, we divide it into right - triangles (by drawing an altitude from the vertex of the acute angle to the opposite side) to use trigonometric ratios.
• Any type: Trigonometric ratios are not directly applicable to non - right triangles without further decomposition into right - triangles.

Since trigonometric ratios have their fundamental definitions in right - triangles, the answer is right triangle.

Answer:

B. right triangle