https://file.aiquickdraw.com/mathbot/file/1730205569678wjnkyapf.jpg

The image you've provided contains two triangles with the task to find the lengths of the missing sides for each triangle.

### Triangle A:
Sides provided:
- \( AB = 6 \)
- \( BC = 8 \)
- \( AC = ? \)

Since this appears to be a right triangle (judging by the labeling and angles), we can use the **Pythagorean theorem**:
\[
AB^2 + BC^2 = AC^2
\]
\[
6^2 + 8^2 = AC^2
\]
\[
36 + 64 = AC^2
\]
\[
100 = AC^2
\]
\[
AC = \sqrt{100} = 10
\]

So, the missing side \( AC \) is \( 10 \).

### Triangle B:
Sides provided:
- \( DE = 9 \)
- \( EF = 12 \)
- \( DF = ? \)

Using the **Pythagorean theorem** again (assuming this is also a right triangle):
\[
DE^2 + EF^2 = DF^2
\]
\[
9^2 + 12^2 = DF^2
\]
\[
81 + 144 = DF^2
\]
\[
225 = DF^2
\]
\[
DF = \sqrt{225} = 15
\]

So, the missing side \( DF \) is \( 15 \).

### Summary of Results:
- For Triangle A: \( AC = 10 \)
- For Triangle B: \( DF = 15 \)

Would you like further details or explanations on any step?

---

#### Related Questions:
1. How would you solve for a missing side if the triangle wasn't a right triangle?
2. What are the properties of a right triangle?
3. How does the Pythagorean theorem apply to different types of triangles?
4. Can the Pythagorean theorem be used in three-dimensional space?
5. How can you verify if a triangle is a right triangle given side lengths?

#### Tip:
Always check if a triangle has a right angle before using the Pythagorean theorem; it only applies to right triangles!

Find the lengths of the missing sides in each triangle.

Solve for the missing side lengths in two right triangles using the Pythagorean theorem. This problem demonstrates key geometry concepts suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation