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Question 1

A)
Use the equation to find the length of the missing leg measure.



NOTE: Type in numerical answers only to receive credit.

(3 points)
a2+162=202
1. Evaluate the powers: a2+
$$=400
2. Isolate the variable: a2=
$$

3. Take the square root of both sides: a2−−√=144−−−√
4. The missing side length is a=
$$

Question 2
A)
On a recent test, Shawna was given the following problem:

Shawna's work is shown below:

Step 1: a2+72=252
Step 2: a2+14=50
Step 3: a2=36
a=6 m
In which step did Shawna make an error?

(1 point)
Responses

Step 1. She incorrectly applied the Pythagorean theorem.
Step 1. She incorrectly applied the Pythagorean theorem.

Step 4. She incorrectly solved for a
Step 4. She incorrectly solved for A

Step 3. She incorrectly isolated a2
Step 3. She incorrectly isolated A squared

Step 2. She incorrectly squared the numbers.
Step 2. She incorrectly squared the numbers.
Question 3
A)Which right triangle has an unknown leg measure of 43−−√
? (1 point)
Responses

Question 4
A)
A set of stairs is being built according to the drawing:

What is the height of one stair?

(1 point)
Responses

12−−√
in.
square root of 12 in.

12 in.
12 in.

36 in.
36 in.

144 in.
144 in.
Question 5
A)
A ladder that is 22 feet long is leaning against a 15-foot tall wall. Label the photo with the correct side lengths based on the given information.

*Note, you will have to solve for the missing side.

(3 points)
Drop target 1
Drop target 2
Drop target 3

1 answer

Let's answer each question step by step.

Question 1

A)

Given the equation \( a^2 + 162 = 202 \), let's solve for \( a \).

  1. Evaluate the powers: \[ a^2 + 162 = 202 \]

  2. Isolate the variable: \[ a^2 = 202 - 162 = 40 \]

  3. Take the square root of both sides: \[ a = \sqrt{40} = \sqrt{4 \cdot 10} = 2\sqrt{10} \]

  4. The missing side length is: \[ a = 2\sqrt{10} \approx 6.32 \text{ (Numerical answer should be entered if required)} \]

Question 2

A)

Shawna's work:

  1. Step 1: \( a^2 + 72 = 252 \)
  2. Step 2: \( a^2 + 14 = 50 \)
  3. Step 3: \( a^2 = 36 \)
  4. Step 4: \( a = 6 \text{ m} \)

In which step did Shawna make an error?

Response: Step 1. She incorrectly applied the Pythagorean theorem.

Question 3

A)

Which right triangle has an unknown leg measure of \( \sqrt{43} \)?

Since multiple triangles could feature \( \sqrt{43} \), I cannot specifically answer without additional information. Please provide details if there's a relevant triangle or context.

Question 4

A)

What is the height of one stair?

If a right triangle represents the stairs, and typical dimensions are involved (like 36 inches implies a standard height), without specific dimensions or additional context, it is reasonable to consider:

Responses: 12 in. (if a simpler interpretation is applied) or If taken as one step per the diagram, 12 in. could represent the rise per step.

Question 5

A)

Given that a ladder is 22 feet long and leaning against a 15-foot tall wall, we can use the Pythagorean theorem to find the base (ground) distance from the wall.

  1. Using \( a^2 + b^2 = c^2 \):

    • Here, \( a = 15 \) (height)
    • \( c = 22 \) (ladder length)
    • \( b = ? \) (distance from wall)

  2. Plug in values: \[ 15^2 + b^2 = 22^2 \] \[ 225 + b^2 = 484 \] \[ b^2 = 484 - 225 \] \[ b^2 = 259 \] \[ b \approx \sqrt{259} \approx 16.1 \text{ feet} \]

Label with correct lengths:

  • Drop target 1: 15 ft (height)
  • Drop target 2: \( \sqrt{259} \) ft (horizontal distance, approx. 16.1 ft)
  • Drop target 3: 22 ft (length of the ladder)

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