The image shows a large triangle divided into three right triangles. Each triangle has dimensions labeled for one of its legs and its hypotenuse, while some values are missing.

Here's a breakdown of the given values:

1. Leftmost triangle:

   • Legs: 10 and 12
   • Hypotenuse is missing.

2. Middle triangle:

   • Legs: 15 and 8
   • Hypotenuse is missing.

3. Rightmost triangle:

   • Legs: 12.5 and the missing leg is part of the large triangle's height
   • Hypotenuse: 20

To solve for the missing sides, we can use the Pythagorean theorem:

$a^2 + b^2 = c^2$

Let me solve each one step-by-step.

Solution:

1. Leftmost Triangle Hypotenuse (c): $10^2 + 12^2 = c^2$ $100 + 144 = c^2$ $c = \sqrt{244} \approx 15.62$

2. Middle Triangle Hypotenuse (c): $15^2 + 8^2 = c^2$ $225 + 64 = c^2$ $c = \sqrt{289} = 17$

3. Rightmost Triangle Missing Leg (b): Using the hypotenuse of 20 and one leg of 12.5: $12.5^2 + b^2 = 20^2$ $156.25 + b^2 = 400$ $b^2 = 243.75$ $b = \sqrt{243.75} \approx 15.61$

Summary of Missing Values:

• Leftmost triangle hypotenuse ≈ 15.62
• Middle triangle hypotenuse = 17
• Rightmost triangle missing leg ≈ 15.61

Would you like further details or explanations for any step?

Here are 5 related questions to expand on this concept:

1. How does the Pythagorean theorem apply to different types of triangles?
2. How can we calculate the area of each triangle individually?
3. How does understanding similar triangles help in solving complex problems?
4. Can we use trigonometric ratios to solve for missing sides in right triangles?
5. What are real-life applications of the Pythagorean theorem?

Tip: When working with right triangles, always ensure the values satisfy the Pythagorean theorem to confirm the triangle is a right triangle.