Math Problem Statement

Julian describes an angle in the triangle using these statements. GH is the adjacent side. HK is the opposite side. GK is the hypotenuse. Which angle(s) is Julian describing?

Solution

To solve the problem:

Key Points from the Question:

  • GH is the adjacent side.
  • HK is the opposite side.
  • GK is the hypotenuse.

Step-by-Step Solution:

  1. Understand the Triangle:

    • The hypotenuse (GK) is always the longest side of the triangle.
    • The adjacent side (GH) is the side next to the angle being referenced but is not the hypotenuse.
    • The opposite side (HK) is the side across from the angle being referenced.
  2. Identifying the Angle:

    • If GH is adjacent, HK is opposite, and GK is the hypotenuse, we are describing ∠G. This is because:
      • GH (adjacent) lies next to ∠G.
      • HK (opposite) is across from ∠G.
      • GK remains the hypotenuse for the entire triangle.
  3. Conclusion:

    • Julian is describing ∠G.

Final Answer:

The correct choice is: ∠G.


Would you like additional details on trigonometric relationships or further clarification? Here are some related questions to deepen understanding:

  1. How do you determine the opposite, adjacent, and hypotenuse for a given angle in any right triangle?
  2. What are the sine, cosine, and tangent ratios, and how do they relate to the sides of a triangle?
  3. Can this method of identifying angles and sides be applied to non-right triangles? If not, why?
  4. Why is the hypotenuse always the longest side of a right triangle?
  5. How would you describe the other angles (∠H and ∠K) in this triangle based on their sides?

Tip: Remember, the key to identifying angles in right triangles is correctly labeling the sides relative to the angle of interest.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle

Formulas

Definition of adjacent, opposite, and hypotenuse sides

Theorems

Pythagorean theorem (indirectly related)
Trigonometric relationships in right triangles

Suitable Grade Level

Grades 8-10