Geometry

Question Analysis

The main focus is to determine the correct trigonometric ratio for finding the unknown side in a right - triangle, based on the identification of the sides relative to the angle. This requires a firm grasp of sine, cosine, and tangent definitions.

Key Concept Explanation

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

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

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

Step - by - Step Solution

1. Identify the sides relative to the angle:

Given that is the opposite side and 33 is the hypotenuse.

2. Match with the trigonometric ratio:

Using the definition of sine, since , substituting , opposite side = , and hypotenuse = 33, we get