For the right triangle shown below, correctly label the sides(3 points)

Question

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. \( AE \approx 35.2 \)