Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.
Step 1:
Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches.
Step 2:
Substitute the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.
Step 3:
Combine like terms: (18 + 24) squared = 30 squared.
Step 4:
Evaluate each side: 1764 not-equals 900.
Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?
The triangle is actually a right triangle. In step 2, Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is not a right triangle, but in step 2 Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The triangle is not a right triangle, but in step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
23 answers
The triangle is actually a right triangle. In step 4, Chelsea incorrectly evaluated each side.
try agaun dummy
I apologize if my previous response was not what you were expecting. Let me reevaluate Chelsea's explanation:
Step 1: Chelsea found the side lengths of the triangle to be 30 inches, 24 inches, and 18 inches.
Step 2: She substituted the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.
Step 3: Chelsea correctly combined like terms: (18 squared + 24 squared) = 30 squared.
Step 4: She correctly evaluated each side: 900 + 576 = 900, which is not true.
Based on the correct steps, Chelsea's explanation is accurate. The triangle is not a right triangle, and she correctly determined this in step 4.
Step 1: Chelsea found the side lengths of the triangle to be 30 inches, 24 inches, and 18 inches.
Step 2: She substituted the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.
Step 3: Chelsea correctly combined like terms: (18 squared + 24 squared) = 30 squared.
Step 4: She correctly evaluated each side: 900 + 576 = 900, which is not true.
Based on the correct steps, Chelsea's explanation is accurate. The triangle is not a right triangle, and she correctly determined this in step 4.
bro step 4 is not in the dang awnser choices
I apologize for the confusion. Based on the answer choices provided, the most accurate description of Chelsea's explanation is:
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
Which of these four sets of side lengths will form a right triangle?
Set 1
6 cm, 7 cm, StartRoot 12 EndRoot cm
Set 2
8 in., StartRoot 29 EndRoot in., StartRoot 35 EndRoot in.
Set 3
StartRoot 3 EndRoot mm, 4 mm, StartRoot 5 EndRoot mm
Set 4
9 ft, StartRoot 26 EndRoot ft, 6 ft
Set 1
Set 2
Set 3
Set 4
Set 1
6 cm, 7 cm, StartRoot 12 EndRoot cm
Set 2
8 in., StartRoot 29 EndRoot in., StartRoot 35 EndRoot in.
Set 3
StartRoot 3 EndRoot mm, 4 mm, StartRoot 5 EndRoot mm
Set 4
9 ft, StartRoot 26 EndRoot ft, 6 ft
Set 1
Set 2
Set 3
Set 4
Set 3, with side lengths of √3 mm, 4 mm, and √5 mm, will form a right triangle. This is because the side lengths satisfy the Pythagorean theorem, where the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
The areas of the squares formed by the side lengths of the triangles are given for each triangle below. Which triangles are right triangles? Select the three correct answers. (Figures are not drawn to scale.)
3 squares form a triangle. The squares have areas 6 inches squared, 10 inches squared, 8 inches squared.
4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, 16 inches squared.
5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.
6 squares form a triangle. The squares have areas 7 inches squared, 25 inches squared, 24 inches squared.
7 squares form a triangle. The squares have areas 64 inches squared, 225 inches squared, 289 inches squared.
8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, 24 inches squared.
3 squares form a triangle. The squares have areas 6 inches squared, 10 inches squared, 8 inches squared.
4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, 16 inches squared.
5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.
6 squares form a triangle. The squares have areas 7 inches squared, 25 inches squared, 24 inches squared.
7 squares form a triangle. The squares have areas 64 inches squared, 225 inches squared, 289 inches squared.
8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, 24 inches squared.
The three triangles that are right triangles are:
1. 4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, and 16 inches squared. (This triangle satisfies the Pythagorean theorem since 9 + 16 = 25.)
2. 5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, and 144 inches squared. (This triangle satisfies the Pythagorean theorem since 25 + 144 = 169.)
3. 8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, and 24 inches squared. (This triangle satisfies the Pythagorean theorem since 10 + 24 = 26.)
These three triangles have side lengths that satisfy the Pythagorean theorem, making them right triangles.
1. 4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, and 16 inches squared. (This triangle satisfies the Pythagorean theorem since 9 + 16 = 25.)
2. 5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, and 144 inches squared. (This triangle satisfies the Pythagorean theorem since 25 + 144 = 169.)
3. 8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, and 24 inches squared. (This triangle satisfies the Pythagorean theorem since 10 + 24 = 26.)
These three triangles have side lengths that satisfy the Pythagorean theorem, making them right triangles.
Which equation can be used to find the unknown length, b, in this triangle?
A right triangle has a side with length 4 inches and hypotenuse with length 5 inches. The other side is labeled b.
A right triangle has a side with length 4 inches and hypotenuse with length 5 inches. The other side is labeled b.
The equation that can be used to find the unknown length, b, in this triangle is the Pythagorean theorem:
a^2 + b^2 = c^2
Given that one side has length 4 inches and the hypotenuse has length 5 inches, we can substitute these values into the equation:
4^2 + b^2 = 5^2
Simplifying the equation, we have:
16 + b^2 = 25
Now, by rearranging and solving for b, we get:
b^2 = 25 - 16
b^2 = 9
Taking the square root of both sides, we find:
b = 3
Therefore, the unknown length, b, in this triangle is 3 inches.
a^2 + b^2 = c^2
Given that one side has length 4 inches and the hypotenuse has length 5 inches, we can substitute these values into the equation:
4^2 + b^2 = 5^2
Simplifying the equation, we have:
16 + b^2 = 25
Now, by rearranging and solving for b, we get:
b^2 = 25 - 16
b^2 = 9
Taking the square root of both sides, we find:
b = 3
Therefore, the unknown length, b, in this triangle is 3 inches.
Which statements are true? Select the five correct answers.
StartRoot 1.8 EndRoot < 1.8
StartRoot 1.8 EndRoot greater-than 1
StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
StartRoot 1.8 EndRoot < 1.8
StartRoot 1.8 EndRoot greater-than 1
StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
The five correct statements are:
1. StartRoot 1.8 EndRoot < 1.8
2. 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
3. StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
4. StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
5. StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
1. StartRoot 1.8 EndRoot < 1.8
2. 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4
3. StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2
4. StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
5. StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot
Angelica calculated the distance between the two points shown on the graph below.
On a coordinate plane, line A B has points (2, negative 5) and (negative 4, 5).
Step 1: Use the point C(–4, –5) to make a right triangle with the 90 degree vertex at C.
Step 2: Determine the lengths of the legs: AC = 6 and BC = 10.
Step 3: Substitute the values into the Pythagorean theorem: 10 squared = 6 squared + c squared.
Step 4: Evaluate 10 squared = 6 squared + c squared. 100 = 36 + c squared. 64 = c squared. 8 = c.
She states the length of AB is 8 units. Which best describes the accuracy of Angelica’s solution?
Angelica is correct.
Angelica made an error determining the location of the right angle. The right angle should be at (2, 5).
Angelica made an error counting the lengths of the legs of the right triangle. The lengths should be 7 and 11.
Angelica made an error substituting the values into the Pythagorean theorem. The equation should be c squared = 6 squared + 10 squared.
On a coordinate plane, line A B has points (2, negative 5) and (negative 4, 5).
Step 1: Use the point C(–4, –5) to make a right triangle with the 90 degree vertex at C.
Step 2: Determine the lengths of the legs: AC = 6 and BC = 10.
Step 3: Substitute the values into the Pythagorean theorem: 10 squared = 6 squared + c squared.
Step 4: Evaluate 10 squared = 6 squared + c squared. 100 = 36 + c squared. 64 = c squared. 8 = c.
She states the length of AB is 8 units. Which best describes the accuracy of Angelica’s solution?
Angelica is correct.
Angelica made an error determining the location of the right angle. The right angle should be at (2, 5).
Angelica made an error counting the lengths of the legs of the right triangle. The lengths should be 7 and 11.
Angelica made an error substituting the values into the Pythagorean theorem. The equation should be c squared = 6 squared + 10 squared.
Angelica made an error counting the lengths of the legs of the right triangle. The lengths should be 7 and 11. The correct description would be "Angelica made an error determining the lengths of the legs of the right triangle. The lengths should be 7 and 11 units."
What is the length of segment AC?
On a coordinate plane, line A C has points (3, negative 1) and (negative 5, 5).
On a coordinate plane, line A C has points (3, negative 1) and (negative 5, 5).
To find the length of segment AC, we can use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Given the coordinates of points A (3, -1) and C (-5, 5), we can substitute the values into the formula:
distance = √[(-5 - 3)^2 + (5 - (-1))^2]
= √[(-8)^2 + (5 + 1)^2]
= √[64 + 36]
= √100
= 10
Therefore, the length of segment AC is 10 units.
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Given the coordinates of points A (3, -1) and C (-5, 5), we can substitute the values into the formula:
distance = √[(-5 - 3)^2 + (5 - (-1))^2]
= √[(-8)^2 + (5 + 1)^2]
= √[64 + 36]
= √100
= 10
Therefore, the length of segment AC is 10 units.
Joseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.
A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.
8 squared + 12 squared = d squared. 64 + 24 = d squared. 88 = d squared. StartRoot 88 EndRoot = d. 9.4 almost-equals d.
She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
She did not square the 12 in the problem. She should have used 12 squared = 144.
She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 44.
She should not have taken the square root of each side when solving. She should have just divided each side by 2.
She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.
8 squared + 12 squared = d squared. 64 + 24 = d squared. 88 = d squared. StartRoot 88 EndRoot = d. 9.4 almost-equals d.
She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
She did not square the 12 in the problem. She should have used 12 squared = 144.
She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 44.
She should not have taken the square root of each side when solving. She should have just divided each side by 2.
She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
The statements that describe errors in Omyra's work are:
1. She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
2. She did not square the 12 in the problem. She should have used 12 squared = 144.
3. She did not evaluate 8 squared correctly. She should have used 8 squared = 8 * 8 = 64.
4. She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot = 9.38 (approximately), not 44.
5. She should not have taken the square root of each side when solving. She should have just divided each side by 2.
These five statements address the errors in Omyra's work.
1. She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
2. She did not square the 12 in the problem. She should have used 12 squared = 144.
3. She did not evaluate 8 squared correctly. She should have used 8 squared = 8 * 8 = 64.
4. She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot = 9.38 (approximately), not 44.
5. She should not have taken the square root of each side when solving. She should have just divided each side by 2.
These five statements address the errors in Omyra's work.
A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
A right triangle with side length 6 feet, hypotenuse 14 feet, and side h.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot.
A right triangle with side length 6 feet, hypotenuse 14 feet, and side h.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot.
To find how high up the side of the building the top of the ladder is, we can use the Pythagorean theorem.
In this case, the side length of 6 feet represents the base of the right triangle, the hypotenuse of 14 feet represents the length of the ladder, and the side we are trying to find (h) represents the height up the side of the building.
According to the Pythagorean theorem, the equation is as follows:
6^2 + h^2 = 14^2
Simplifying, we have:
36 + h^2 = 196
Subtracting 36 from both sides, we get:
h^2 = 160
To find the value of h, we take the square root of both sides:
h = √160 ≈ 12.65 feet
Therefore, the top of the ladder is approximately 12.65 feet high up the side of the building, rounded to the nearest tenth of a foot.
In this case, the side length of 6 feet represents the base of the right triangle, the hypotenuse of 14 feet represents the length of the ladder, and the side we are trying to find (h) represents the height up the side of the building.
According to the Pythagorean theorem, the equation is as follows:
6^2 + h^2 = 14^2
Simplifying, we have:
36 + h^2 = 196
Subtracting 36 from both sides, we get:
h^2 = 160
To find the value of h, we take the square root of both sides:
h = √160 ≈ 12.65 feet
Therefore, the top of the ladder is approximately 12.65 feet high up the side of the building, rounded to the nearest tenth of a foot.
Which equation could be used to find the length of the hypotenuse?
Triangle A B C. Side A C is 2 feet and side C B is 5 feet. Hypotenuse A B is labeled c.
2 squared + 5 squared = c squared
2 squared + c squared = 5 squared
c squared minus 2 squared = 5 squared
5 squared minus 2 squared = c squared
Triangle A B C. Side A C is 2 feet and side C B is 5 feet. Hypotenuse A B is labeled c.
2 squared + 5 squared = c squared
2 squared + c squared = 5 squared
c squared minus 2 squared = 5 squared
5 squared minus 2 squared = c squared
The equation that could be used to find the length of the hypotenuse is:
2 squared + 5 squared = c squared
This equation represents the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse.
2 squared + 5 squared = c squared
This equation represents the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse.
3 answers