Question

For the right triangle shown below, correctly label the sides(3 points)
Drop target 1
Drop target 2
Drop target 3
Question 2
If CE = 29 and AC = 20, which of the following equations can be used to find AE?(2 points)
Responses

20+x=29
20 plus x is equal to 29

20+29=x
20 plus 29 is equal to x

202+x2=292
20 squared plus x squared is equal to 29 squared

202+292=x2
20 squared plus 29 squared is equal to x squared
Question 3
Using the information given above, find AE. Round to the nearest tenth if necessary.(2 points)
AE =

Answer 1

To answer your questions, let’s start with labeling the right triangle and then move to the equations for finding \( AE \) and then calculating its value.

### Question 1: Labeling the Sides
Typically, in a right triangle, we label:
- \( AC \) as one leg (let's say it’s the shorter leg),
- \( CE \) as the other leg (the longer leg),
- \( AE \) as the hypotenuse.

In your case:
- So, label: \( AC = 20 \) (one leg)
- Label: \( CE = 29 \) (other leg)
- Label: \( AE \) (hypotenuse)

### Question 2: Finding AE with Equations
Given \( CE = 29 \) and \( AC = 20 \), we need to find \( AE \). The Pythagorean theorem states:
\[
AE^2 = AC^2 + CE^2
\]

This leads us to:
- \( AE^2 = 20^2 + 29^2 \)

So the correct equation from the options you provided is:
- \( 20^2 + 29^2 = x^2 \)
- **Answer**: \( 20^2 + 29^2 = x^2 \)

### Question 3: Finding AE
Now we can calculate \( AE \):

1. Calculate \( AC^2 \) and \( CE^2 \):
- \( 20^2 = 400 \)
- \( 29^2 = 841 \)

2. Sum these values:
- \( 400 + 841 = 1241 \)

3. Take the square root to find \( AE \):
- \( AE = \sqrt{1241} \approx 35.2 \)

So, rounded to the nearest tenth, \( AE \) is:
- **AE = 35.2**

### Summary Answers:
1. Label sides: \( AC = 20, CE = 29, AE \) (hypotenuse)
2. Correct equation: \( 20^2 + 29^2 = x^2 \)
3. \( AE \approx 35.2 \)