Geometry

Question Analysis

The key of this question is to figure out the appropriate trigonometric ratio for finding the unknown side  based on the relationship between the sides and the given angle. A precise understanding of sine, cosine, and tangent definitions in right - triangles is required.

Key Concept Explanation

Sine (sin): In a right - triangle, , where  is an acute angle, the opposite side is directly 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:

If the side with length 9 is the opposite side to the  angle, and the side  is the hypotenuse.

2. Match with the trigonometric ratio:

According to the definition of sine, . Substituting , the opposite side = 9, and the hypotenuse = , we obtain .