https://r2.erweima.ai/mathbot/image/17259381202087is35hgi.jpg

I see that you've uploaded an image with various triangles labeled with different dimensions. Let's go over each triangle one by one to solve for the unknowns.

### 1. First Triangle (Right Triangle)
- **Sides given**: 11 cm, 14 cm.
- **Unknown**: \( t \), the third side (adjacent).

This is a right triangle, so we can use the **Pythagorean theorem**:
\[
a^2 + b^2 = c^2
\]
Where \( c = 14 \, \text{cm} \) (hypotenuse), and \( a = 11 \, \text{cm} \).

### 2. Second Triangle (Isosceles Triangle)
- **Given**: Two equal sides of 9 cm, base of 8 cm.
- **Unknown**: Height \( h \).

We can use the **Pythagorean theorem** by splitting the isosceles triangle into two right triangles. The base is divided into two equal parts of 4 cm each, and the height \( h \) is the unknown.

### 3. Third Triangle (Right Triangle)
- **Given**: Legs of 5 m and hypotenuse of 13 m.
- **Unknown**: Height \( p \).

Again, we use the **Pythagorean theorem** to find \( p \).

### 4. Fourth Triangle (Right Triangle)
- **Given**: Hypotenuse of 4.3 cm and one leg of 2.3 cm.
- **Unknown**: Other leg \( y \).

We apply the **Pythagorean theorem** here.

### 5. Fifth Triangle (Right Triangle with height and bases)
- **Given**: Total base is 9 m, height of 8 m.
- **Unknown**: The slant height \( d \).

Here, we can use the **Pythagorean theorem** on the right triangle formed with height 8 m, half the base (6 m), and slant height \( d \).

### 6. Sixth Triangle (Two right triangles)
- **Given**: Two right triangles combined; the sides of 3 m, 4 m, and 12 m.
- **Unknown**: Side \( f \).

We solve using the **Pythagorean theorem** on the right triangle involving \( f \).

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Would you like me to solve these one at a time with full details, or would you prefer the answers directly for each triangle?

The user provided an image with six different triangles, each labeled with some dimensions. The goal is to find the unknown sides or heights of the triangles using geometric methods like the Pythagorean theorem.

This problem involves solving for unknown sides and heights in various triangles using the Pythagorean theorem. Explore step-by-step solutions for right triangles, isosceles triangles, and more. Suitable for students in Grades 7-9.

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