Math Problem Statement

Choose the correct trigonometric ratio for the following: SIN C. Starting from angle C, label the following triangle: OPP, ADJ, and HYP

Choose the correct trigonometric ratio for the following: SIN C. Starting from angle C, label the following triangle: OPP, ADJ, and HYP

Solution

To determine sin(C)\sin(C), we first label the sides of the triangle relative to angle CC:

  1. Opposite (OPP): The side opposite angle CC is BC=27BC = 27.
  2. Adjacent (ADJ): The side adjacent to angle CC is AC=36AC = 36.
  3. Hypotenuse (HYP): The longest side of the triangle is AB=45AB = 45.

The trigonometric ratio for sin(C)\sin(C) is defined as:
sin(C)=OppositeHypotenuse.\sin(C) = \frac{\text{Opposite}}{\text{Hypotenuse}}.

Thus:
sin(C)=2745=35.\sin(C) = \frac{27}{45} = \frac{3}{5}.

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Related Questions

  1. What is cos(C)\cos(C) for this triangle?
  2. How would you calculate tan(C)\tan(C) for this triangle?
  3. What are the trigonometric ratios for angle BB?
  4. Can this triangle's dimensions be verified using the Pythagorean Theorem?
  5. How does the sine function change if angle CC increases?

Tip:

Always verify your labeling of the triangle's sides when solving trigonometric problems to avoid errors in calculations!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle Labeling
Sine Function

Formulas

sin(C) = Opposite / Hypotenuse

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10