Geometry

Question Analysis

The main focus of this question is to determine the correct trigonometric ratio among the given options for the angles  and  in a right - triangle. It requires a clear understanding of the definitions of sine, cosine, and tangent and accurate identification of the opposite, adjacent, and hypotenuse sides relative to the given angles.

Key Concept Explanation

Sine (sin): In a right - triangle, , where  is an acute angle, the opposite side is the side directly opposite to , and the hypotenuse is the longest side of the triangle.

Cosine (cos): , with the adjacent side being the side next to  (excluding the hypotenuse).

Tangent (tan): , relating the opposite side and the adjacent side of the angle .

Step - by - Step Solution

1. For :

The side adjacent to  is , and the hypotenuse is . Using the formula , we get .

2. For :

The side opposite to  is , and the hypotenuse is

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