Geometry

Question Analysis

The main focus 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): , where  is an acute angle, the opposite side is opposite to , and the hypotenuse is the longest side.

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

Tangent (tan): .

Step - by - Step Solution

1. Identify the sides relative to the  angle:

The side with length 17 is adjacent to the  angle, and the side  is the hypotenuse.

2. Match with the trigonometric ratio:

Using the definition of cosine, since , substituting , adjacent side = 17, and hypotenuse = , we get

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