Trigonometric Ratios Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Trigonometric Ratios" with several right triangles and questions about identifying the sides relative to a given angle (likely labeled as θ). However, I can't view or analyze images directly. But based on your description and the typical structure of such worksheets, I can help you solve it if you describe the triangles and the questions.

Here’s how we can proceed:

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🔍 Common Structure of This Type of Worksheet:

For each triangle (usually labeled with angles and sides), you're asked to identify:
- The side opposite to angle θ
- The side adjacent to angle θ
- The hypotenuse

Then, sometimes you’re asked to write trigonometric ratios like:
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent

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✔ How to Solve It:

Let me walk you through the steps for one triangle (you can apply this to all):

#### Step 1: Identify the Right Angle
- In a right triangle, the hypotenuse is always the side opposite the right angle (the longest side).

#### Step 2: Locate Angle θ
- Find the angle marked as θ (often in one of the acute angles).

#### Step 3: Label the Sides Relative to θ
- Opposite side: the side that is across from θ (not touching it).
- Adjacent side: the side that forms θ along with the hypotenuse (touches θ but is not the hypotenuse).
- Hypotenuse: the side opposite the right angle.

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📌 Example:

Suppose in a right triangle:
- The right angle is at C.
- Angle θ is at A.
- Side BC is opposite to A.
- Side AC is adjacent to A.
- Side AB is the hypotenuse.

Then:
- The leg opposite to θ is BC
- The leg adjacent to θ is AC
- The hypotenuse is AB

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💡 Tips:

- Always label the triangle first.
- Use "SOHCAHTOA":
- Sin = Opposite / Hypotenuse
- Cos = Adjacent / Hypotenuse
- Tan = Opposite / Adjacent

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📝 What You Can Do Now:

Please describe each triangle in the image by providing:
1. Which angle is θ?
2. What are the labels of the sides (e.g., AB, BC, AC)?
3. Or just describe the triangle (e.g., “a right triangle with legs 3 and 4, hypotenuse 5, and θ at the corner between the leg of length 3 and the hypotenuse”)

Then I’ll help you fill in the blanks for each question!

Alternatively, if you can copy-paste the text from the worksheet, I can solve it step-by-step.