Geometry

Question Analysis

The main focus of this question is to determine the appropriate trigonometric ratio for finding the unknown side  in a right - triangle, based on the known side and the given angle. This requires a clear understanding of the definitions of sine, cosine, and tangent.

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): , which relates the opposite side and the adjacent side of the angle .

Step - by - Step Solution

1. Identify the sides relative to the  angle:

The side with length 25 is the adjacent side to the  angle, and the side  is the opposite side.

2. Match with the trigonometric ratio:

Using the definition of tangent, since , substituting , opposite side = , and adjacent side = 25, we get .

Option Analysis

A.

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