4-Isosceles and Equilateral Triangles Problems - Kuta Software ... - Free Printable

It looks like you've uploaded a worksheet titled "Right Triangles: Special Right Triangles" with several geometry problems involving right triangles. However, I can't see the actual image or its contents directly. But based on your description and typical content of such worksheets, I’ll help you solve common problems related to special right triangles, which usually include:

- 45°-45°-90° triangles
- 30°-60°-90° triangles

These are special because their side ratios are consistent and can be derived using the Pythagorean Theorem.

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🔷 Common Side Ratios:

1. 45°-45°-90° Triangle
- Legs are equal.
- Hypotenuse = leg × √2
- Ratio: $ 1 : 1 : \sqrt{2} $

2. 30°-60°-90° Triangle
- Shorter leg (opposite 30°) = x
- Longer leg (opposite 60°) = $ x\sqrt{3} $
- Hypotenuse (opposite 90°) = $ 2x $
- Ratio: $ 1 : \sqrt{3} : 2 $

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Let’s assume the worksheet contains problems like these (common types):

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✔ Example Problem 1:

Find the missing side in a 45°-45°-90° triangle where one leg is 7.

Solution:
Since both legs are equal, the other leg is also 7.
Hypotenuse = $ 7\sqrt{2} $

✔ Answer: $ 7\sqrt{2} $

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✔ Example Problem 2:

In a 30°-60°-90° triangle, the hypotenuse is 10. Find the shorter leg and longer leg.

Solution:
Hypotenuse = $ 2x = 10 $ → $ x = 5 $
- Shorter leg (opposite 30°) = $ x = 5 $
- Longer leg (opposite 60°) = $ x\sqrt{3} = 5\sqrt{3} $

✔ Answers:
- Shorter leg: 5
- Longer leg: $ 5\sqrt{3} $

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✔ Example Problem 3:

A right triangle has angles 30°, 60°, and 90°. The side opposite 30° is 4. What is the hypotenuse?

Solution:
Side opposite 30° = $ x = 4 $
Hypotenuse = $ 2x = 8 $

✔ Answer: 8

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✔ Example Problem 4:

Find the missing side in a right triangle with legs 6 and 6.

This is a 45°-45°-90° triangle.
Hypotenuse = $ 6\sqrt{2} $

✔ Answer: $ 6\sqrt{2} $

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If you can describe or list the specific problems from your image (e.g., "Problem 1: In triangle ABC, angle A is 45°, AB = 8, find AC"), I can give exact solutions.

Alternatively, if you can describe the diagrams or write out the problems, I’ll solve them step by step with explanations.

Let me know!