Trigonometry Worksheet 1 with labeled triangles and tangent ratio formulas.

It looks like you've uploaded a trigonometry worksheet titled *"Trigonometry Worksheet 1"*, which focuses on the tangent (tan) ratio in right-angled triangles. The worksheet contains a large composite figure made up of multiple similar right-angled triangles, and it asks students to:

1. Measure lengths of sides.
2. Divide the lengths as indicated (opposite/adjacent).
3. Calculate the tangent of angle BAF using those ratios.
4. Round answers to 2 decimal places.

However, due to the watermark and overlay text ("CALCULUS", "SUBSCRIBE NOW"), the actual measurements and specific values are obscured — so I can't extract exact numerical data from the image.

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Let’s walk through how to solve this type of problem:

#### 🔷 Objective:
Find `tan(∠BAF)` using the tangent ratio:
> tan(θ) = opposite / adjacent

In triangle BAF, angle BAF is at point A, so:
- The opposite side to ∠BAF is BF
- The adjacent side is AF

So:
> tan(∠BAF) = BF / AF

Similarly, since all the triangles are similar, we can use any of the smaller triangles that share the same angle (like triangle CGH or DIH) to find the same tangent ratio.

For example:
- In triangle CGH: tan(∠BAF) = CG / AG
- In triangle DIH: tan(∠BAF) = DI / AI

Because the triangles are similar, these ratios should be equal (or very close if measured manually).

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✔ Steps to Solve:

1. Measure the lengths (using a ruler):
- Measure BF and AF → then compute BF/AF
- Measure CG and AG → compute CG/AG
- Measure DI and AI → compute DI/AI

2. Divide each pair and record the result in the boxes.

3. Round to 2 decimal places.

4. Since all triangles are similar, all three ratios should give approximately the same value for tan(∠BAF).

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📌 Example (hypothetical):

Suppose your measurements are:
- BF = 2.5 cm
- AF = 4.0 cm
→ BF/AF = 2.5 / 4.0 = 0.625 ≈ 0.63

- CG = 3.75 cm
- AG = 6.0 cm
→ CG/AG = 3.75 / 6.0 = 0.625 ≈ 0.63

- DI = 5.0 cm
- AI = 8.0 cm
→ DI/AI = 5.0 / 8.0 = 0.625 ≈ 0.63

Then:
> tan(∠BAF) = 0.63

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💡 Key Concept:

The tangent ratio depends only on the angle, not the size of the triangle. Since all triangles are similar, they have the same angles and thus the same tangent values.

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❗But...

Since the image has a large watermark covering the actual diagram, I cannot see:
- The scale or actual measurements
- The positions of points
- Whether the diagram is drawn to scale

Therefore, I cannot provide exact numbers unless you:
- Describe the measurements
- Provide the actual values from the worksheet
- Or upload a clearer version without the watermark

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✔ What You Can Do Now:

If you can measure the lengths yourself (with a ruler), follow these steps:

1. Use a ruler to measure:
- BF, AF
- CG, AG
- DI, AI

2. Compute each ratio:
- BF/AF
- CG/AG
- DI/AI

3. Write down each to 2 decimal places

4. All should be equal (within measurement error)

5. That common value is tan(∠BAF)

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Would you like me to help you calculate it if you provide the measured lengths? Just tell me what you got for:
- BF, AF
- CG, AG
- DI, AI

And I’ll do the rest!