Math Problem Statement

The question asks to name the missing side x in \(\triangle ABC\), with the reference angle at A.

Solution

The question asks to name the missing side xx in ABC\triangle ABC, with the reference angle at AA. Here's how to approach this:

  1. In a right triangle, the sides are named relative to the reference angle:

    • Opposite: The side opposite the reference angle.
    • Adjacent: The side next to the reference angle that is not the hypotenuse.
    • Hypotenuse: The side opposite the right angle (the longest side).
  2. Observing the diagram:

    • The hypotenuse is labeled as 11 (side ABAB).
    • The side xx is directly opposite the reference angle AA, making it the opposite side.

Correct answer:

Opposite

Would you like a detailed explanation of how to classify triangle sides or more practice problems?


Related Questions:

  1. What is the definition of the adjacent side in a right triangle?
  2. How do you calculate the missing side length in a right triangle using trigonometric ratios?
  3. How do you identify the hypotenuse in any right triangle?
  4. Why is the hypotenuse always the longest side in a right triangle?
  5. Can the adjacent and opposite sides ever have the same length in a right triangle?

Tip:

Remember, labeling sides relative to a reference angle is essential in using trigonometric functions like sine, cosine, and tangent.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangles
Side Classification

Formulas

Pythagorean Theorem
Trigonometric ratios (sine, cosine, tangent)

Theorems

Sine, cosine, and tangent functions in right triangles

Suitable Grade Level

Grades 7-9