Practice worksheet for solving right triangle problems using trigonometry.

It looks like you've uploaded a worksheet titled "Geometry – Trig Ratios in Right Triangles", which includes several problems involving right triangles and trigonometric ratios (sine, cosine, tangent). Since I can't view images directly, I'll help you solve the problems based on what's typically found in such worksheets.

Let me walk through how to solve these types of problems step by step. If you can describe or list the specific problems (e.g., side lengths, angles, or question numbers), I can give precise answers. But here’s a general guide and solutions for common problems on this type of worksheet:

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🔷 General Strategy:

For each right triangle problem:
1. Identify the given parts: two sides or one side and one acute angle.
2. Use the appropriate trig ratio:
- Sine = opposite / hypotenuse
- Cosine = adjacent / hypotenuse
- Tangent = opposite / adjacent
3. Set up the equation using the known values.
4. Solve for the unknown.
5. Round to the nearest tenth if required.

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🔷 Example Problems & Solutions

Let’s assume the worksheet has the following typical problems (based on standard formats):

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#### Problem 1:
Triangle with:
- Hypotenuse = 10
- One leg = 6
- Find the missing leg.

✔ Use Pythagorean Theorem:
$$
a^2 + b^2 = c^2 \\
6^2 + x^2 = 10^2 \\
36 + x^2 = 100 \\
x^2 = 64 \\
x = \sqrt{64} = 8
$$

👉 Missing side = 8

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#### Problem 2:
Right triangle with:
- Angle A = 30°
- Side opposite = 5
- Find hypotenuse.

Use sine:
$$
\sin(30^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{x} \\
\sin(30^\circ) = 0.5 \\
0.5 = \frac{5}{x} \\
x = \frac{5}{0.5} = 10
$$

👉 Hypotenuse = 10

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#### Problem 3:
Find angle θ where:
- Opposite = 12
- Adjacent = 9

Use tangent:
$$
\tan(\theta) = \frac{12}{9} = 1.333... \\
\theta = \tan^{-1}(1.333...) \approx 53.1^\circ
$$

👉 Angle ≈ 53.1°

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#### Problem 10 (Kite Problem):
> A kite is flying at a height of 20 feet. The string makes a 60° angle with the ground. How long is the string?

This is a right triangle:
- Opposite side = 20 ft (height)
- Angle = 60°
- Hypotenuse = string length (unknown)

Use sine:
$$
\sin(60^\circ) = \frac{20}{x} \\
\sin(60^\circ) \approx 0.866 \\
0.866 = \frac{20}{x} \\
x = \frac{20}{0.866} \approx 23.1
$$

👉 String length ≈ 23.1 feet

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#### Problem 11 (Ladder Problem):
> A ladder leans against a wall. It’s 10 ft long and reaches 8 ft up the wall. What angle does it make with the ground?

Given:
- Hypotenuse = 10 ft
- Opposite = 8 ft

Use sine:
$$
\sin(\theta) = \frac{8}{10} = 0.8 \\
\theta = \sin^{-1}(0.8) \approx 53.1^\circ
$$

👉 Angle ≈ 53.1°

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✔ Final Tips:

- Always label the triangle: opposite, adjacent, hypotenuse relative to the angle.
- Use SOHCAHTOA as a memory aid.
- Use inverse functions ($\sin^{-1}$, $\cos^{-1}$, $\tan^{-1}$) when solving for angles.
- Round final answers to the nearest tenth as instructed.

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If you can tell me the exact values from your worksheet (e.g., side lengths, angles, or question numbers), I can solve them precisely.

Would you like to describe any specific problem from the image? For example:
- "In problem #7, there’s a triangle with angle 45°, side 12, find the other side..."
Then I’ll solve it exactly!